48x=100+x^2

Solution for 48x=100+x^2 equation:

48x=100+x^2

We move all terms to the left:

48x-(100+x^2)=0

We get rid of parentheses

-x^2+48x-100=0

We add all the numbers together, and all the variables

-1x^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}
$