3z2+2=10

Solution for 3z2+2=10 equation:

3z^2+2=10

We move all terms to the left:

3z^2+2-(10)=0

We add all the numbers together, and all the variables

3z^2-8=0

a = 3; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·3·(-8)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*3}=\frac{0-4\sqrt{6}}{6}
=-\frac{4\sqrt{6}}{6}
=-\frac{2\sqrt{6}}{3}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*3}=\frac{0+4\sqrt{6}}{6}
=\frac{4\sqrt{6}}{6}
=\frac{2\sqrt{6}}{3}
$