24=x*x+5x

Solution for 24=x*x+5x equation:

24=x*x+5x

We move all terms to the left:

24-(x*x+5x)=0

We add all the numbers together, and all the variables

-(+5x+x*x)+24=0

We get rid of parentheses

-5x-x*x+24=0

Wy multiply elements

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