9×2-5x=3

Move 3 to the left side of the equation by subtracting it from both sides.

9×2-5x-3=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=9, b=-5, and c=-3 into the quadratic formula and solve for x.

5±(-5)2-4⋅(9⋅-3)2⋅9

Simplify the numerator.

Raise -5 to the power of 2.

x=5±25-4⋅(9⋅-3)2⋅9

Multiply 9 by -3.

x=5±25-4⋅-272⋅9

Multiply -4 by -27.

x=5±25+1082⋅9

Add 25 and 108.

x=5±1332⋅9

x=5±1332⋅9

Multiply 2 by 9.

x=5±13318

x=5±13318

The final answer is the combination of both solutions.

x=5+13318,5-13318

The result can be shown in multiple forms.

Exact Form:

x=5+13318,5-13318

Decimal Form:

x=0.91847569…,-0.36292014…

Solve for x 9x^2-5x=3