12z=144-6z^2

Solution for 12z=144-6z^2 equation:

12z=144-6z^2

We move all terms to the left:

12z-(144-6z^2)=0

We get rid of parentheses

6z^2+12z-144=0

a = 6; b = 12; c = -144;
Δ = b2-4ac
Δ = 122-4·6·(-144)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-60}{2*6}=\frac{-72}{12}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+60}{2*6}=\frac{48}{12}
=4
$