36=0.5(3x+12)(x+2)

Solution for 36=0.5(3x+12)(x+2) equation:

36=0.5(3x+12)(x+2)

We move all terms to the left:

36-(0.5(3x+12)(x+2))=0

We multiply parentheses ..

-(0.5(+3x^2+6x+12x+24))+36=0


We calculate terms in parentheses: -(0.5(+3x^2+6x+12x+24)), so:

0.5(+3x^2+6x+12x+24)

We multiply parentheses

1.5x^2+3x+6x+12

We add all the numbers together, and all the variables

1.5x^2+9x+12

Back to the equation:

-(1.5x^2+9x+12)


We get rid of parentheses

-1.5x^2-9x-12+36=0

We add all the numbers together, and all the variables

-1.5x^2-9x+24=0

a = -1.5; b = -9; c = +24;
Δ = b2-4ac
Δ = -92-4·(-1.5)·24
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*-1.5}=\frac{-6}{-3}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*-1.5}=\frac{24}{-3}
=-8
$