z^2+10z=20

Solution for z^2+10z=20 equation:

z^2+10z=20

We move all terms to the left:

z^2+10z-(20)=0

a = 1; b = 10; c = -20;
Δ = b2-4ac
Δ = 102-4·1·(-20)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*1}=\frac{-10-6\sqrt{5}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*1}=\frac{-10+6\sqrt{5}}{2}
$