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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

(+3x^2+6x+12x+24)-72=0

We get rid of parentheses

3x^2+6x+12x+24-72=0

We add all the numbers together, and all the variables

3x^2+18x-48=0

a = 3; b = 18; c = -48;
Δ = b2-4ac
Δ = 182-4·3·(-48)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*3}=\frac{12}{6}
=2
$