x^2-4x+8=33

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

x^2-4x+8=33

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2-4x-25=0

a = 1; b = -4; c = -25;
Δ = b2-4ac
Δ = -42-4·1·(-25)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{29}}{2*1}=\frac{4-2\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{29}}{2*1}=\frac{4+2\sqrt{29}}{2}
$