6x+12=(x+2)(2x-1)

Solution for 6x+12=(x+2)(2x-1) equation:

6x+12=(x+2)(2x-1)

We move all terms to the left:

6x+12-((x+2)(2x-1))=0

We multiply parentheses ..

-((+2x^2-1x+4x-2))+6x+12=0


We calculate terms in parentheses: -((+2x^2-1x+4x-2)), so:

(+2x^2-1x+4x-2)

We get rid of parentheses

2x^2-1x+4x-2

We add all the numbers together, and all the variables

2x^2+3x-2

Back to the equation:

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


We add all the numbers together, and all the variables

6x-(2x^2+3x-2)+12=0

We get rid of parentheses

-2x^2+6x-3x+2+12=0

We add all the numbers together, and all the variables

-2x^2+3x+14=0

a = -2; b = 3; c = +14;
Δ = b2-4ac
Δ = 32-4·(-2)·14
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-11}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+11}{2*-2}=\frac{8}{-4}
=-2
$