x^2-13x+33=11

Solution for x^2-13x+33=11 equation:

x^2-13x+33=11

We move all terms to the left:

x^2-13x+33-(11)=0

We add all the numbers together, and all the variables

x^2-13x+22=0

a = 1; b = -13; c = +22;
Δ = b2-4ac
Δ = -132-4·1·22
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-9}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+9}{2*1}=\frac{22}{2}
=11
$