3z+z*z=180

Solution for 3z+z*z=180 equation:

3z+z*z=180

We move all terms to the left:

3z+z*z-(180)=0

Wy multiply elements

z^2+3z-180=0

a = 1; b = 3; c = -180;
Δ = b2-4ac
Δ = 32-4·1·(-180)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*1}=\frac{-30}{2}
=-15
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*1}=\frac{24}{2}
=12
$