x^2-28x=-33

Solution for x^2-28x=-33 equation:

x^2-28x=-33

We move all terms to the left:

x^2-28x-(-33)=0

We add all the numbers together, and all the variables

x^2-28x+33=0

a = 1; b = -28; c = +33;
Δ = b2-4ac
Δ = -282-4·1·33
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{163}}{2*1}=\frac{28-2\sqrt{163}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{163}}{2*1}=\frac{28+2\sqrt{163}}{2}
$