24=(x+5)(x)

Solution for 24=(x+5)(x) equation:

24=(x+5)(x)

We move all terms to the left:

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


We calculate terms in parentheses: -((x+5)x), so:

(x+5)x

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


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