-5z=12-4z^2

Solution for -5z=12-4z^2 equation:

-5z=12-4z^2

We move all terms to the left:

-5z-(12-4z^2)=0

We get rid of parentheses

4z^2-5z-12=0

a = 4; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·4·(-12)
Δ = 217
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{217}}{2*4}=\frac{5-\sqrt{217}}{8}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*4}=\frac{5+\sqrt{217}}{8}
$