-4a^2-33a=-8

Solution for -4a^2-33a=-8 equation:

-4a^2-33a=-8

We move all terms to the left:

-4a^2-33a-(-8)=0

We add all the numbers together, and all the variables

-4a^2-33a+8=0

a = -4; b = -33; c = +8;
Δ = b2-4ac
Δ = -332-4·(-4)·8
Δ = 1217
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{-(-33)-\sqrt{1217}}{2*-4}=\frac{33-\sqrt{1217}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1217}}{2*-4}=\frac{33+\sqrt{1217}}{-8}
$