3z^2=155

Solution for 3z^2=155 equation:

3z^2=155

We move all terms to the left:

3z^2-(155)=0

a = 3; b = 0; c = -155;
Δ = b2-4ac
Δ = 02-4·3·(-155)
Δ = 1860
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:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{465}}{2*3}=\frac{0-2\sqrt{465}}{6}
=-\frac{2\sqrt{465}}{6}
=-\frac{\sqrt{465}}{3}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{465}}{2*3}=\frac{0+2\sqrt{465}}{6}
=\frac{2\sqrt{465}}{6}
=\frac{\sqrt{465}}{3}
$