2y-8=6-2y^2

Solution for 2y-8=6-2y^2 equation:

2y-8=6-2y^2

We move all terms to the left:

2y-8-(6-2y^2)=0

We get rid of parentheses

2y^2+2y-6-8=0

We add all the numbers together, and all the variables

2y^2+2y-14=0

a = 2; b = 2; c = -14;
Δ = b2-4ac
Δ = 22-4·2·(-14)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{29}}{2*2}=\frac{-2-2\sqrt{29}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{29}}{2*2}=\frac{-2+2\sqrt{29}}{4}
$