-8g^2+8g+22=8

Solution for -8g^2+8g+22=8 equation:

-8g^2+8g+22=8

We move all terms to the left:

-8g^2+8g+22-(8)=0

We add all the numbers together, and all the variables

-8g^2+8g+14=0

a = -8; b = 8; c = +14;
Δ = b2-4ac
Δ = 82-4·(-8)·14
Δ = 512
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{2}}{2*-8}=\frac{-8-16\sqrt{2}}{-16}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{2}}{2*-8}=\frac{-8+16\sqrt{2}}{-16}
$