/3x+12=20+2x

Solution for /3x+12=20+2x equation:

/3x+12=20+2x

We move all terms to the left:

/3x+12-(20+2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

/3x-(2x+20)+12=0

We get rid of parentheses

/3x-2x-20+12=0

We multiply all the terms by the denominator


-2x*3x-20*3x+12*3x+=0

We add all the numbers together, and all the variables

-2x*3x-20*3x+12*3x=0

Wy multiply elements

-6x^2-60x+36x=0

We add all the numbers together, and all the variables

-6x^2-24x=0

a = -6; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-6)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-6}=\frac{48}{-12}
=-4
$