z^2-20z=17

Solution for z^2-20z=17 equation:

z^2-20z=17

We move all terms to the left:

z^2-20z-(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:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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