4x^2-48x+1=0

Solution for 4x^2-48x+1=0 equation:

4x^2-48x+1=0

a = 4; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·4·1
Δ = 2288
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:

$\sqrt{\Delta}=\sqrt{2288}=\sqrt{16*143}=\sqrt{16}*\sqrt{143}=4\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{143}}{2*4}=\frac{48-4\sqrt{143}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{143}}{2*4}=\frac{48+4\sqrt{143}}{8}
$