48x=(x^2)+24

Solution for 48x=(x^2)+24 equation:

48x=(x^2)+24

We move all terms to the left:

48x-((x^2)+24)=0

We get rid of parentheses

-x^2+48x-24=0

We add all the numbers together, and all the variables

-1x^2+48x-24=0

a = -1; b = 48; c = -24;
Δ = b2-4ac
Δ = 482-4·(-1)·(-24)
Δ = 2208
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:

$\sqrt{\Delta}=\sqrt{2208}=\sqrt{16*138}=\sqrt{16}*\sqrt{138}=4\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{138}}{2*-1}=\frac{-48-4\sqrt{138}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{138}}{2*-1}=\frac{-48+4\sqrt{138}}{-2}
$