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

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

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

We multiply parentheses

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

We add all the numbers together, and all the variables

5y^2+43y-42=0

a = 5; b = 43; c = -42;
Δ = b2-4ac
Δ = 432-4·5·(-42)
Δ = 2689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-\sqrt{2689}}{2*5}=\frac{-43-\sqrt{2689}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{2689}}{2*5}=\frac{-43+\sqrt{2689}}{10}
$