3/3x-12=x+126

Solution for 3/3x-12=x+126 equation:

3/3x-12=x+126

We move all terms to the left:

3/3x-12-(x+126)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

3/3x-x-126-12=0

We multiply all the terms by the denominator


-x*3x-126*3x-12*3x+3=0

Wy multiply elements

-3x^2-378x-36x+3=0

We add all the numbers together, and all the variables

-3x^2-414x+3=0

a = -3; b = -414; c = +3;
Δ = b2-4ac
Δ = -4142-4·(-3)·3
Δ = 171432
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:

$\sqrt{\Delta}=\sqrt{171432}=\sqrt{36*4762}=\sqrt{36}*\sqrt{4762}=6\sqrt{4762}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-414)-6\sqrt{4762}}{2*-3}=\frac{414-6\sqrt{4762}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-414)+6\sqrt{4762}}{2*-3}=\frac{414+6\sqrt{4762}}{-6}
$