9y(6y+15)=25

Solution for 9y(6y+15)=25 equation:

9y(6y+15)=25

We move all terms to the left:

9y(6y+15)-(25)=0

We multiply parentheses

54y^2+135y-25=0

a = 54; b = 135; c = -25;
Δ = b2-4ac
Δ = 1352-4·54·(-25)
Δ = 23625
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:

$\sqrt{\Delta}=\sqrt{23625}=\sqrt{225*105}=\sqrt{225}*\sqrt{105}=15\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-15\sqrt{105}}{2*54}=\frac{-135-15\sqrt{105}}{108}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+15\sqrt{105}}{2*54}=\frac{-135+15\sqrt{105}}{108}
$