-x2+9x=18x+x2

Solution for -x2+9x=18x+x2 equation:

-x2+9x=18x+x2

We move all terms to the left:

-x2+9x-(18x+x2)=0

We add all the numbers together, and all the variables

-(+18x+x^2)-x2+9x=0

We add all the numbers together, and all the variables

-1x^2-(+18x+x^2)+9x=0

We get rid of parentheses

-1x^2-x^2-18x+9x=0

We add all the numbers together, and all the variables

-2x^2-9x=0

a = -2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-2)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-2}=\frac{18}{-4}
=-4+1/2
$