5y^2-6y-9=0

Solution for 5y^2-6y-9=0 equation:

5y^2-6y-9=0

a = 5; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·5·(-9)
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{6}}{2*5}=\frac{6-6\sqrt{6}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{6}}{2*5}=\frac{6+6\sqrt{6}}{10}
$