x^2-8x-33=10

Solution for x^2-8x-33=10 equation:

x^2-8x-33=10

We move all terms to the left:

x^2-8x-33-(10)=0

We add all the numbers together, and all the variables

x^2-8x-43=0

a = 1; b = -8; c = -43;
Δ = b2-4ac
Δ = -82-4·1·(-43)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{59}}{2*1}=\frac{8-2\sqrt{59}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{59}}{2*1}=\frac{8+2\sqrt{59}}{2}
$