4z^2-76=0

Solution for 4z^2-76=0 equation:

4z^2-76=0

a = 4; b = 0; c = -76;
Δ = b2-4ac
Δ = 02-4·4·(-76)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{19}}{2*4}=\frac{0-8\sqrt{19}}{8}
=-\frac{8\sqrt{19}}{8}
=-\sqrt{19}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{19}}{2*4}=\frac{0+8\sqrt{19}}{8}
=\frac{8\sqrt{19}}{8}
=\sqrt{19}
$