2y^2+2y(y-8)=13

Solution for 2y^2+2y(y-8)=13 equation:

2y^2+2y(y-8)=13

We move all terms to the left:

2y^2+2y(y-8)-(13)=0

We multiply parentheses

2y^2+2y^2-16y-13=0

We add all the numbers together, and all the variables

4y^2-16y-13=0

a = 4; b = -16; c = -13;
Δ = b2-4ac
Δ = -162-4·4·(-13)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{29}}{2*4}=\frac{16-4\sqrt{29}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{29}}{2*4}=\frac{16+4\sqrt{29}}{8}
$