Find the Roots (Zeros) -10x^2+12x-9=0

$- 10 x^{2} + 12 x - 9 = 0$

Factor $- 1$ out of $- 10 x^{2} + 12 x - 9$ .

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Factor $- 1$ out of $- 10 x^{2}$ .

$- (10 x^{2}) + 12 x - 9 = 0$

Factor $- 1$ out of $12 x$ .

$- (10 x^{2}) - (- 12 x) - 9 = 0$

Rewrite $- 9$ as $- 1 (9)$ .

$- (10 x^{2}) - (- 12 x) - 1 \cdot 9 = 0$

Factor $- 1$ out of $- (10 x^{2}) - (- 12 x)$ .

$- (10 x^{2} - 12 x) - 1 \cdot 9 = 0$

Factor $- 1$ out of $- (10 x^{2} - 12 x) - 1 (9)$ .

$- (10 x^{2} - 12 x + 9) = 0$

Multiply each term in $- (10 x^{2} - 12 x + 9) = 0$ by $- 1$

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Multiply each term in $- (10 x^{2} - 12 x + 9) = 0$ by $- 1$ .

$- (10 x^{2} - 12 x + 9) \cdot - 1 = 0 \cdot - 1$

Simplify $- (10 x^{2} - 12 x + 9) \cdot - 1$ .

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Apply the distributive property.

$(- (10 x^{2}) - (- 12 x) - 1 \cdot 9) \cdot - 1 = 0 \cdot - 1$

Simplify.

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Multiply $10$ by $- 1$ .

$(- 10 x^{2} - (- 12 x) - 1 \cdot 9) \cdot - 1 = 0 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$(- 10 x^{2} + 12 x - 1 \cdot 9) \cdot - 1 = 0 \cdot - 1$

Multiply $- 1$ by $9$ .

$(- 10 x^{2} + 12 x - 9) \cdot - 1 = 0 \cdot - 1$

Apply the distributive property.

$- 10 x^{2} \cdot - 1 + 12 x \cdot - 1 - 9 \cdot - 1 = 0 \cdot - 1$

Simplify.

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Multiply $- 1$ by $- 10$ .

$10 x^{2} + 12 x \cdot - 1 - 9 \cdot - 1 = 0 \cdot - 1$

Multiply $- 1$ by $12$ .

$10 x^{2} - 12 x - 9 \cdot - 1 = 0 \cdot - 1$

Multiply $- 9$ by $- 1$ .

$10 x^{2} - 12 x + 9 = 0 \cdot - 1$

Multiply $0$ by $- 1$ .

$10 x^{2} - 12 x + 9 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 10$ , $b = - 12$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{12 \pm \sqrt{{(- 12)}^{2} - 4 \cdot (10 \cdot 9)}}{2 \cdot 10}$

Simplify.

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Simplify the numerator.

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Raise $- 12$ to the power of $2$ .

$x = \frac{12 \pm \sqrt{144 - 4 \cdot (10 \cdot 9)}}{2 \cdot 10}$

Multiply $10$ by $9$ .

$x = \frac{12 \pm \sqrt{144 - 4 \cdot 90}}{2 \cdot 10}$

Multiply $- 4$ by $90$ .

$x = \frac{12 \pm \sqrt{144 - 360}}{2 \cdot 10}$

Subtract $360$ from $144$ .

$x = \frac{12 \pm \sqrt{- 216}}{2 \cdot 10}$

Rewrite $- 216$ as $- 1 (216)$ .

$x = \frac{12 \pm \sqrt{- 1 \cdot 216}}{2 \cdot 10}$

Rewrite $\sqrt{- 1 (216)}$ as $\sqrt{- 1} \cdot \sqrt{216}$ .

$x = \frac{12 \pm \sqrt{- 1} \cdot \sqrt{216}}{2 \cdot 10}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{12 \pm i \cdot \sqrt{216}}{2 \cdot 10}$

Rewrite $216$ as $6^{2} \cdot 6$ .

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Factor $36$ out of $216$ .

$x = \frac{12 \pm i \cdot \sqrt{36 (6)}}{2 \cdot 10}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{12 \pm i \cdot \sqrt{6^{2} \cdot 6}}{2 \cdot 10}$

Pull terms out from under the radical.

$x = \frac{12 \pm i \cdot (6 \sqrt{6})}{2 \cdot 10}$

Move $6$ to the left of $i$ .

$x = \frac{12 \pm 6 i \sqrt{6}}{2 \cdot 10}$

Multiply $2$ by $10$ .

$x = \frac{12 \pm 6 i \sqrt{6}}{20}$

Simplify $\frac{12 \pm 6 i \sqrt{6}}{20}$ .

$x = \frac{6 \pm 3 i \sqrt{6}}{10}$

Find the Roots (Zeros) -10x^2+12x-9=0

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