-1/3x+12=-2x+2

Solution for -1/3x+12=-2x+2 equation:

-1/3x+12=-2x+2

We move all terms to the left:

-1/3x+12-(-2x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x+2x-2+12=0

We multiply all the terms by the denominator


2x*3x-2*3x+12*3x-1=0

Wy multiply elements

6x^2-6x+36x-1=0

We add all the numbers together, and all the variables

6x^2+30x-1=0

a = 6; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·6·(-1)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{231}}{2*6}=\frac{-30-2\sqrt{231}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{231}}{2*6}=\frac{-30+2\sqrt{231}}{12}
$