76=4x^2

Solution for 76=4x^2 equation:

76=4x^2

We move all terms to the left:

76-(4x^2)=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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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