(x)=x(x+24)

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

(x)=x(x+24)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(x+24)), so:

x(x+24)

We multiply parentheses

x^2+24x

Back to the equation:

-(x^2+24x)


We get rid of parentheses

-x^2+x-24x=0

We add all the numbers together, and all the variables

-1x^2-23x=0

a = -1; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-1)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-1}=\frac{46}{-2}
=-23
$