X^2-48x+100=0

Solution for X^2-48x+100=0 equation:

X^2-48X+100=0

a = 1; b = -48; c = +100;
Δ = b2-4ac
Δ = -482-4·1·100
Δ = 1904
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:

$\sqrt{\Delta}=\sqrt{1904}=\sqrt{16*119}=\sqrt{16}*\sqrt{119}=4\sqrt{119}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{119}}{2*1}=\frac{48-4\sqrt{119}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{119}}{2*1}=\frac{48+4\sqrt{119}}{2}
$