a^2+3a-3=8

Solution for a^2+3a-3=8 equation:

a^2+3a-3=8

We move all terms to the left:

a^2+3a-3-(8)=0

We add all the numbers together, and all the variables

a^2+3a-11=0

a = 1; b = 3; c = -11;
Δ = b2-4ac
Δ = 32-4·1·(-11)
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{53}}{2*1}=\frac{-3-\sqrt{53}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{53}}{2*1}=\frac{-3+\sqrt{53}}{2}
$