X^2-20x+100=17

Solution for X^2-20x+100=17 equation:

X^2-20X+100=17

We move all terms to the left:

X^2-20X+100-(17)=0

We add all the numbers together, and all the variables

X^2-20X+83=0

a = 1; b = -20; c = +83;
Δ = b2-4ac
Δ = -202-4·1·83
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{17}}{2*1}=\frac{20-2\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{17}}{2*1}=\frac{20+2\sqrt{17}}{2}
$