-6y(y+15)=-3y+6

Solution for -6y(y+15)=-3y+6 equation:

-6y(y+15)=-3y+6

We move all terms to the left:

-6y(y+15)-(-3y+6)=0

We multiply parentheses

-6y^2-90y-(-3y+6)=0

We get rid of parentheses

-6y^2-90y+3y-6=0

We add all the numbers together, and all the variables

-6y^2-87y-6=0

a = -6; b = -87; c = -6;
Δ = b2-4ac
Δ = -872-4·(-6)·(-6)
Δ = 7425
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:

$\sqrt{\Delta}=\sqrt{7425}=\sqrt{225*33}=\sqrt{225}*\sqrt{33}=15\sqrt{33}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87)-15\sqrt{33}}{2*-6}=\frac{87-15\sqrt{33}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+15\sqrt{33}}{2*-6}=\frac{87+15\sqrt{33}}{-12}
$