X2-20x-17=3

Solution for X2-20x-17=3 equation:

X2-20X-17=3

We move all terms to the left:

X2-20X-17-(3)=0

We add all the numbers together, and all the variables

X^2-20X-20=0

a = 1; b = -20; c = -20;
Δ = b2-4ac
Δ = -202-4·1·(-20)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{30}}{2*1}=\frac{20-4\sqrt{30}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{30}}{2*1}=\frac{20+4\sqrt{30}}{2}
$