9x-(x-18)=2x(9+x)

Solution for 9x-(x-18)=2x(9+x) equation:

9x-(x-18)=2x(9+x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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


We calculate terms in parentheses: -(2x(x+9)), so:

2x(x+9)

We multiply parentheses

2x^2+18x

Back to the equation:

-(2x^2+18x)


We add all the numbers together, and all the variables

8x-(2x^2+18x)+18=0

We get rid of parentheses

-2x^2+8x-18x+18=0

We add all the numbers together, and all the variables

-2x^2-10x+18=0

a = -2; b = -10; c = +18;
Δ = b2-4ac
Δ = -102-4·(-2)·18
Δ = 244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{61}}{2*-2}=\frac{10-2\sqrt{61}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{61}}{2*-2}=\frac{10+2\sqrt{61}}{-4}
$