9y(6y+15)=180

Solution for 9y(6y+15)=180 equation:

9y(6y+15)=180

We move all terms to the left:

9y(6y+15)-(180)=0

We multiply parentheses

54y^2+135y-180=0

a = 54; b = 135; c = -180;
Δ = b2-4ac
Δ = 1352-4·54·(-180)
Δ = 57105
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:

$\sqrt{\Delta}=\sqrt{57105}=\sqrt{81*705}=\sqrt{81}*\sqrt{705}=9\sqrt{705}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-9\sqrt{705}}{2*54}=\frac{-135-9\sqrt{705}}{108}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+9\sqrt{705}}{2*54}=\frac{-135+9\sqrt{705}}{108}
$