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
