X^2-20x+17=0

Solution for X^2-20x+17=0 equation:

X^2-20X+17=0

a = 1; b = -20; c = +17;
Δ = b2-4ac
Δ = -202-4·1·17
Δ = 332
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:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{83}}{2*1}=\frac{20-2\sqrt{83}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{83}}{2*1}=\frac{20+2\sqrt{83}}{2}
$