15y(10y+24)=180

Solution for 15y(10y+24)=180 equation:

15y(10y+24)=180

We move all terms to the left:

15y(10y+24)-(180)=0

We multiply parentheses

150y^2+360y-180=0

a = 150; b = 360; c = -180;
Δ = b2-4ac
Δ = 3602-4·150·(-180)
Δ = 237600
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:

$\sqrt{\Delta}=\sqrt{237600}=\sqrt{3600*66}=\sqrt{3600}*\sqrt{66}=60\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-60\sqrt{66}}{2*150}=\frac{-360-60\sqrt{66}}{300}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+60\sqrt{66}}{2*150}=\frac{-360+60\sqrt{66}}{300}
$