x^2-8x-33=5

Solution for x^2-8x-33=5 equation:

x^2-8x-33=5

We move all terms to the left:

x^2-8x-33-(5)=0

We add all the numbers together, and all the variables

x^2-8x-38=0

a = 1; b = -8; c = -38;
Δ = b2-4ac
Δ = -82-4·1·(-38)
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{6}}{2*1}=\frac{8-6\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{6}}{2*1}=\frac{8+6\sqrt{6}}{2}
$