z^2+5z=9

Solution for z^2+5z=9 equation:

z^2+5z=9

We move all terms to the left:

z^2+5z-(9)=0

a = 1; b = 5; c = -9;
Δ = b2-4ac
Δ = 52-4·1·(-9)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{61}}{2*1}=\frac{-5-\sqrt{61}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{61}}{2*1}=\frac{-5+\sqrt{61}}{2}
$