2/3x-4=12+x

Solution for 2/3x-4=12+x equation:

2/3x-4=12+x

We move all terms to the left:

2/3x-4-(12+x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(x+12)-4=0

We get rid of parentheses

2/3x-x-12-4=0

We multiply all the terms by the denominator


-x*3x-12*3x-4*3x+2=0

Wy multiply elements

-3x^2-36x-12x+2=0

We add all the numbers together, and all the variables

-3x^2-48x+2=0

a = -3; b = -48; c = +2;
Δ = b2-4ac
Δ = -482-4·(-3)·2
Δ = 2328
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:

$\sqrt{\Delta}=\sqrt{2328}=\sqrt{4*582}=\sqrt{4}*\sqrt{582}=2\sqrt{582}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{582}}{2*-3}=\frac{48-2\sqrt{582}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{582}}{2*-3}=\frac{48+2\sqrt{582}}{-6}
$