5x=x^2-24

Solution for 5x=x^2-24 equation:

5x=x^2-24

We move all terms to the left:

5x-(x^2-24)=0

We get rid of parentheses

-x^2+5x+24=0

We add all the numbers together, and all the variables

-1x^2+5x+24=0

a = -1; b = 5; c = +24;
Δ = b2-4ac
Δ = 52-4·(-1)·24
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-1}=\frac{6}{-2}
=-3
$