18x-x^2=x

Solution for 18x-x^2=x equation:

18x-x^2=x

We move all terms to the left:

18x-x^2-(x)=0

We add all the numbers together, and all the variables

-1x^2+17x=0

a = -1; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-1)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-1}=\frac{-34}{-2}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-1}=\frac{0}{-2}
=0
$