8z^2-6=378

Solution for 8z^2-6=378 equation:

8z^2-6=378

We move all terms to the left:

8z^2-6-(378)=0

We add all the numbers together, and all the variables

8z^2-384=0

a = 8; b = 0; c = -384;
Δ = b2-4ac
Δ = 02-4·8·(-384)
Δ = 12288
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:

$\sqrt{\Delta}=\sqrt{12288}=\sqrt{4096*3}=\sqrt{4096}*\sqrt{3}=64\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{3}}{2*8}=\frac{0-64\sqrt{3}}{16}
=-\frac{64\sqrt{3}}{16}
=-4\sqrt{3}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{3}}{2*8}=\frac{0+64\sqrt{3}}{16}
=\frac{64\sqrt{3}}{16}
=4\sqrt{3}
$