x=(2x+3)(x-6)

Solution for x=(2x+3)(x-6) equation:

x=(2x+3)(x-6)

We move all terms to the left:

x-((2x+3)(x-6))=0

We multiply parentheses ..

-((+2x^2-12x+3x-18))+x=0


We calculate terms in parentheses: -((+2x^2-12x+3x-18)), so:

(+2x^2-12x+3x-18)

We get rid of parentheses

2x^2-12x+3x-18

We add all the numbers together, and all the variables

2x^2-9x-18

Back to the equation:

-(2x^2-9x-18)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x^2+x+9x+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}
$