5x=x(18-x)

Solution for 5x=x(18-x) equation:

5x=x(18-x)

We move all terms to the left:

5x-(x(18-x))=0

We add all the numbers together, and all the variables

5x-(x(-1x+18))=0


We calculate terms in parentheses: -(x(-1x+18)), so:

x(-1x+18)

We multiply parentheses

-1x^2+18x

Back to the equation:

-(-1x^2+18x)


We get rid of parentheses

1x^2-18x+5x=0

We add all the numbers together, and all the variables

x^2-13x=0

a = 1; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·1·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*1}=\frac{26}{2}
=13
$