-2y(y-9)=2y+6

Solution for -2y(y-9)=2y+6 equation:

-2y(y-9)=2y+6

We move all terms to the left:

-2y(y-9)-(2y+6)=0

We multiply parentheses

-2y^2+18y-(2y+6)=0

We get rid of parentheses

-2y^2+18y-2y-6=0

We add all the numbers together, and all the variables

-2y^2+16y-6=0

a = -2; b = 16; c = -6;
Δ = b2-4ac
Δ = 162-4·(-2)·(-6)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{13}}{2*-2}=\frac{-16-4\sqrt{13}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{13}}{2*-2}=\frac{-16+4\sqrt{13}}{-4}
$