x2+20x=33

Solution for x2+20x=33 equation:

x2+20x=33

We move all terms to the left:

x2+20x-(33)=0

We add all the numbers together, and all the variables

x^2+20x-33=0

a = 1; b = 20; c = -33;
Δ = b2-4ac
Δ = 202-4·1·(-33)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{133}}{2*1}=\frac{-20-2\sqrt{133}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{133}}{2*1}=\frac{-20+2\sqrt{133}}{2}
$