15(y-4)-2y(y-9)+5(y+6)=0

Solution for 15(y-4)-2y(y-9)+5(y+6)=0 equation:

15(y-4)-2y(y-9)+5(y+6)=0

We multiply parentheses

-2y^2+15y+18y+5y-60+30=0

We add all the numbers together, and all the variables

-2y^2+38y-30=0

a = -2; b = 38; c = -30;
Δ = b2-4ac
Δ = 382-4·(-2)·(-30)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{301}}{2*-2}=\frac{-38-2\sqrt{301}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{301}}{2*-2}=\frac{-38+2\sqrt{301}}{-4}
$