x2-20x=17

Solution for x2-20x=17 equation:

x2-20x=17

We move all terms to the left:

x2-20x-(17)=0

We add all the numbers together, and all the variables

x^2-20x-17=0

a = 1; b = -20; c = -17;
Δ = b2-4ac
Δ = -202-4·1·(-17)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{13}}{2*1}=\frac{20-6\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{13}}{2*1}=\frac{20+6\sqrt{13}}{2}
$