8z2=14

Solution for 8z2=14 equation:

8z^2=14

We move all terms to the left:

8z^2-(14)=0

a = 8; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·8·(-14)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*8}=\frac{0-8\sqrt{7}}{16}
=-\frac{8\sqrt{7}}{16}
=-\frac{\sqrt{7}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*8}=\frac{0+8\sqrt{7}}{16}
=\frac{8\sqrt{7}}{16}
=\frac{\sqrt{7}}{2}
$