x=(2x-3)(x+9)

Solution for x=(2x-3)(x+9) equation:

x=(2x-3)(x+9)

We move all terms to the left:

x-((2x-3)(x+9))=0

We multiply parentheses ..

-((+2x^2+18x-3x-27))+x=0


We calculate terms in parentheses: -((+2x^2+18x-3x-27)), so:

(+2x^2+18x-3x-27)

We get rid of parentheses

2x^2+18x-3x-27

We add all the numbers together, and all the variables

2x^2+15x-27

Back to the equation:

-(2x^2+15x-27)


We add all the numbers together, and all the variables

x-(2x^2+15x-27)=0

We get rid of parentheses

-2x^2+x-15x+27=0

We add all the numbers together, and all the variables

-2x^2-14x+27=0

a = -2; b = -14; c = +27;
Δ = b2-4ac
Δ = -142-4·(-2)·27
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{103}}{2*-2}=\frac{14-2\sqrt{103}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{103}}{2*-2}=\frac{14+2\sqrt{103}}{-4}
$