1/3x-12=2x-52

Solution for 1/3x-12=2x-52 equation:

1/3x-12=2x-52

We move all terms to the left:

1/3x-12-(2x-52)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x+52-12=0

We multiply all the terms by the denominator


-2x*3x+52*3x-12*3x+1=0

Wy multiply elements

-6x^2+156x-36x+1=0

We add all the numbers together, and all the variables

-6x^2+120x+1=0

a = -6; b = 120; c = +1;
Δ = b2-4ac
Δ = 1202-4·(-6)·1
Δ = 14424
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:

$\sqrt{\Delta}=\sqrt{14424}=\sqrt{4*3606}=\sqrt{4}*\sqrt{3606}=2\sqrt{3606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3606}}{2*-6}=\frac{-120-2\sqrt{3606}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3606}}{2*-6}=\frac{-120+2\sqrt{3606}}{-12}
$