5y2+6y-3=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=5, b=6, and c=-3 into the quadratic formula and solve for y.

-6±62-4⋅(5⋅-3)2⋅5

Simplify the numerator.

Raise 6 to the power of 2.

y=-6±36-4⋅(5⋅-3)2⋅5

Multiply 5 by -3.

y=-6±36-4⋅-152⋅5

Multiply -4 by -15.

y=-6±36+602⋅5

Add 36 and 60.

y=-6±962⋅5

Rewrite 96 as 42⋅6.

Factor 16 out of 96.

y=-6±16(6)2⋅5

Rewrite 16 as 42.

y=-6±42⋅62⋅5

y=-6±42⋅62⋅5

Pull terms out from under the radical.

y=-6±462⋅5

y=-6±462⋅5

Multiply 2 by 5.

y=-6±4610

Simplify -6±4610.

y=-3±265

y=-3±265

Simplify the numerator.

Raise 6 to the power of 2.

y=-6±36-4⋅(5⋅-3)2⋅5

Multiply 5 by -3.

y=-6±36-4⋅-152⋅5

Multiply -4 by -15.

y=-6±36+602⋅5

Add 36 and 60.

y=-6±962⋅5

Rewrite 96 as 42⋅6.

Factor 16 out of 96.

y=-6±16(6)2⋅5

Rewrite 16 as 42.

y=-6±42⋅62⋅5

y=-6±42⋅62⋅5

Pull terms out from under the radical.

y=-6±462⋅5

y=-6±462⋅5

Multiply 2 by 5.

y=-6±4610

Simplify -6±4610.

y=-3±265

Change the ± to +.

y=-3+265

Rewrite -3 as -1(3).

y=-1⋅3+265

Factor -1 out of 26.

y=-1⋅3-(-26)5

Factor -1 out of -1(3)-(-26).

y=-1(3-26)5

Move the negative in front of the fraction.

y=-3-265

y=-3-265

Simplify the numerator.

Raise 6 to the power of 2.

y=-6±36-4⋅(5⋅-3)2⋅5

Multiply 5 by -3.

y=-6±36-4⋅-152⋅5

Multiply -4 by -15.

y=-6±36+602⋅5

Add 36 and 60.

y=-6±962⋅5

Rewrite 96 as 42⋅6.

Factor 16 out of 96.

y=-6±16(6)2⋅5

Rewrite 16 as 42.

y=-6±42⋅62⋅5

y=-6±42⋅62⋅5

Pull terms out from under the radical.

y=-6±462⋅5

y=-6±462⋅5

Multiply 2 by 5.

y=-6±4610

Simplify -6±4610.

y=-3±265

Change the ± to -.

y=-3-265

Rewrite -3 as -1(3).

y=-1⋅3-265

Factor -1 out of -26.

y=-1⋅3-(26)5

Factor -1 out of -1(3)-(26).

y=-1(3+26)5

Move the negative in front of the fraction.

y=-3+265

y=-3+265

The final answer is the combination of both solutions.

y=-3-265,-3+265

The result can be shown in multiple forms.

Exact Form:

y=-3-265,-3+265

Decimal Form:

y=0.37979589…,-1.57979589…

Solve Using the Square Root Property 5y^2+6y-3=0