3z2-384=138

Solution for 3z2-384=138 equation:

3z^2-384=138

We move all terms to the left:

3z^2-384-(138)=0

We add all the numbers together, and all the variables

3z^2-522=0

a = 3; b = 0; c = -522;
Δ = b2-4ac
Δ = 02-4·3·(-522)
Δ = 6264
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:

$\sqrt{\Delta}=\sqrt{6264}=\sqrt{36*174}=\sqrt{36}*\sqrt{174}=6\sqrt{174}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{174}}{2*3}=\frac{0-6\sqrt{174}}{6}
=-\frac{6\sqrt{174}}{6}
=-\sqrt{174}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{174}}{2*3}=\frac{0+6\sqrt{174}}{6}
=\frac{6\sqrt{174}}{6}
=\sqrt{174}
$