z^2-22z=37

Solution for z^2-22z=37 equation:

z^2-22z=37

We move all terms to the left:

z^2-22z-(37)=0

a = 1; b = -22; c = -37;
Δ = b2-4ac
Δ = -222-4·1·(-37)
Δ = 632
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:

$\sqrt{\Delta}=\sqrt{632}=\sqrt{4*158}=\sqrt{4}*\sqrt{158}=2\sqrt{158}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{158}}{2*1}=\frac{22-2\sqrt{158}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{158}}{2*1}=\frac{22+2\sqrt{158}}{2}
$