8x^2-33x=-4

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

8x^2-33x=-4

We move all terms to the left:

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

We add all the numbers together, and all the variables

8x^2-33x+4=0

a = 8; b = -33; c = +4;
Δ = b2-4ac
Δ = -332-4·8·4
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*8}=\frac{2}{16}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+31}{2*8}=\frac{64}{16}
=4
$