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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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


We calculate terms in parentheses: -(2x(x+18)), so:

2x(x+18)

We multiply parentheses

2x^2+36x

Back to the equation:

-(2x^2+36x)


We add all the numbers together, and all the variables

8x-(2x^2+36x)+18=0

We get rid of parentheses

-2x^2+8x-36x+18=0

We add all the numbers together, and all the variables

-2x^2-28x+18=0

a = -2; b = -28; c = +18;
Δ = b2-4ac
Δ = -282-4·(-2)·18
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{58}}{2*-2}=\frac{28-4\sqrt{58}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{58}}{2*-2}=\frac{28+4\sqrt{58}}{-4}
$