12-2/3x=X-7

Solution for 12-2/3x=X-7 equation:

12-2/3x=x-7

We move all terms to the left:

12-2/3x-(x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-2/3x-x+7+12=0

We multiply all the terms by the denominator


-x*3x+7*3x+12*3x-2=0

Wy multiply elements

-3x^2+21x+36x-2=0

We add all the numbers together, and all the variables

-3x^2+57x-2=0

a = -3; b = 57; c = -2;
Δ = b2-4ac
Δ = 572-4·(-3)·(-2)
Δ = 3225
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:

$\sqrt{\Delta}=\sqrt{3225}=\sqrt{25*129}=\sqrt{25}*\sqrt{129}=5\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-5\sqrt{129}}{2*-3}=\frac{-57-5\sqrt{129}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+5\sqrt{129}}{2*-3}=\frac{-57+5\sqrt{129}}{-6}
$