-8=4x^2+33x

Solution for -8=4x^2+33x equation:

-8=4x^2+33x

We move all terms to the left:

-8-(4x^2+33x)=0

We get rid of parentheses

-4x^2-33x-8=0

a = -4; b = -33; c = -8;
Δ = b2-4ac
Δ = -332-4·(-4)·(-8)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-31}{2*-4}=\frac{2}{-8}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+31}{2*-4}=\frac{64}{-8}
=-8
$