a^2+8a=33

Solution for a^2+8a=33 equation:

a^2+8a=33

We move all terms to the left:

a^2+8a-(33)=0

a = 1; b = 8; c = -33;
Δ = b2-4ac
Δ = 82-4·1·(-33)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-14}{2*1}=\frac{-22}{2}
=-11
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+14}{2*1}=\frac{6}{2}
=3
$