18x=6x+x(x-13)

Solution for 18x=6x+x(x-13) equation:

18x=6x+x(x-13)

We move all terms to the left:

18x-(6x+x(x-13))=0


We calculate terms in parentheses: -(6x+x(x-13)), so:

6x+x(x-13)

We multiply parentheses

x^2+6x-13x

We add all the numbers together, and all the variables

x^2-7x

Back to the equation:

-(x^2-7x)


We get rid of parentheses

-x^2+18x+7x=0

We add all the numbers together, and all the variables

-1x^2+25x=0

a = -1; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-1)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-1}=\frac{-50}{-2}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-1}=\frac{0}{-2}
=0
$