x^2-20*x+170=100

Solution for x^2-20*x+170=100 equation:

x^2-20x+170=100

We move all terms to the left:

x^2-20x+170-(100)=0

We add all the numbers together, and all the variables

x^2-20x+70=0

a = 1; b = -20; c = +70;
Δ = b2-4ac
Δ = -202-4·1·70
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{30}}{2*1}=\frac{20-2\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{30}}{2*1}=\frac{20+2\sqrt{30}}{2}
$