z*147+z*z=60

Solution for z*147+z*z=60 equation:

z*147+z*z=60

We move all terms to the left:

z*147+z*z-(60)=0

Wy multiply elements

z^2+147z-60=0

a = 1; b = 147; c = -60;
Δ = b2-4ac
Δ = 1472-4·1·(-60)
Δ = 21849
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{-(147)-\sqrt{21849}}{2*1}=\frac{-147-\sqrt{21849}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(147)+\sqrt{21849}}{2*1}=\frac{-147+\sqrt{21849}}{2}
$