36z^2=24-5z

Solution for 36z^2=24-5z equation:

36z^2=24-5z

We move all terms to the left:

36z^2-(24-5z)=0

We add all the numbers together, and all the variables

36z^2-(-5z+24)=0

We get rid of parentheses

36z^2+5z-24=0

a = 36; b = 5; c = -24;
Δ = b2-4ac
Δ = 52-4·36·(-24)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-59}{2*36}=\frac{-64}{72}
=-8/9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+59}{2*36}=\frac{54}{72}
=3/4
$