4x2=-8-33x

Solution for 4x2=-8-33x equation:

4x^2=-8-33x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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