3z2-834=138

Solution for 3z2-834=138 equation:

3z^2-834=138

We move all terms to the left:

3z^2-834-(138)=0

We add all the numbers together, and all the variables

3z^2-972=0

a = 3; b = 0; c = -972;
Δ = b2-4ac
Δ = 02-4·3·(-972)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108}{2*3}=\frac{-108}{6}
=-18
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108}{2*3}=\frac{108}{6}
=18
$