65z=5+32z^2

Solution for 65z=5+32z^2 equation:

65z=5+32z^2

We move all terms to the left:

65z-(5+32z^2)=0

We get rid of parentheses

-32z^2+65z-5=0

a = -32; b = 65; c = -5;
Δ = b2-4ac
Δ = 652-4·(-32)·(-5)
Δ = 3585
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{-(65)-\sqrt{3585}}{2*-32}=\frac{-65-\sqrt{3585}}{-64}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{3585}}{2*-32}=\frac{-65+\sqrt{3585}}{-64}
$