33+3z^2=180

Solution for 33+3z^2=180 equation:

33+3z^2=180

We move all terms to the left:

33+3z^2-(180)=0

We add all the numbers together, and all the variables

3z^2-147=0

a = 3; b = 0; c = -147;
Δ = b2-4ac
Δ = 02-4·3·(-147)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42}{2*3}=\frac{-42}{6}
=-7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42}{2*3}=\frac{42}{6}
=7
$