6a^2-8=-8a

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

6a^2-8=-8a

We move all terms to the left:

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

We get rid of parentheses

6a^2+8a-8=0

a = 6; b = 8; c = -8;
Δ = b2-4ac
Δ = 82-4·6·(-8)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*6}=\frac{-24}{12}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*6}=\frac{8}{12}
=2/3
$