48=4x^2

Solution for 48=4x^2 equation:

48=4x^2

We move all terms to the left:

48-(4x^2)=0

a = -4; b = 0; c = +48;
Δ = b2-4ac
Δ = 02-4·(-4)·48
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*-4}=\frac{0-16\sqrt{3}}{-8}
=-\frac{16\sqrt{3}}{-8}
=-\frac{2\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*-4}=\frac{0+16\sqrt{3}}{-8}
=\frac{16\sqrt{3}}{-8}
=\frac{2\sqrt{3}}{-1}
$