8=2a^2+6a

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

8=2a^2+6a

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·(-2)·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*-2}=\frac{-4}{-4}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*-2}=\frac{16}{-4}
=-4
$