4x^2-48x+2=0

Solution for 4x^2-48x+2=0 equation:

4x^2-48x+2=0

a = 4; b = -48; c = +2;
Δ = b2-4ac
Δ = -482-4·4·2
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{142}}{2*4}=\frac{48-4\sqrt{142}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{142}}{2*4}=\frac{48+4\sqrt{142}}{8}
$