x=x^2+8x-33

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

x=x^2+8x-33

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-7x+33=0

a = -1; b = -7; c = +33;
Δ = b2-4ac
Δ = -72-4·(-1)·33
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{181}}{2*-1}=\frac{7-\sqrt{181}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{181}}{2*-1}=\frac{7+\sqrt{181}}{-2}
$