12z^2=90

Solution for 12z^2=90 equation:

12z^2=90

We move all terms to the left:

12z^2-(90)=0

a = 12; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·12·(-90)
Δ = 4320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{30}}{2*12}=\frac{0-12\sqrt{30}}{24}
=-\frac{12\sqrt{30}}{24}
=-\frac{\sqrt{30}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{30}}{2*12}=\frac{0+12\sqrt{30}}{24}
=\frac{12\sqrt{30}}{24}
=\frac{\sqrt{30}}{2}
$