24x=x^2+42

Solution for 24x=x^2+42 equation:

24x=x^2+42

We move all terms to the left:

24x-(x^2+42)=0

We get rid of parentheses

-x^2+24x-42=0

We add all the numbers together, and all the variables

-1x^2+24x-42=0

a = -1; b = 24; c = -42;
Δ = b2-4ac
Δ = 242-4·(-1)·(-42)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{102}}{2*-1}=\frac{-24-2\sqrt{102}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{102}}{2*-1}=\frac{-24+2\sqrt{102}}{-2}
$