0=4x^2-77

Solution for 0=4x^2-77 equation:

0=4x^2-77

We move all terms to the left:

0-(4x^2-77)=0

We add all the numbers together, and all the variables

-(4x^2-77)=0

We get rid of parentheses

-4x^2+77=0

a = -4; b = 0; c = +77;
Δ = b2-4ac
Δ = 02-4·(-4)·77
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{77}}{2*-4}=\frac{0-4\sqrt{77}}{-8}
=-\frac{4\sqrt{77}}{-8}
=-\frac{\sqrt{77}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{77}}{2*-4}=\frac{0+4\sqrt{77}}{-8}
=\frac{4\sqrt{77}}{-8}
=\frac{\sqrt{77}}{-2}
$