3x-6=-6/6x+12

Solution for 3x-6=-6/6x+12 equation:

3x-6=-6/6x+12

We move all terms to the left:

3x-6-(-6/6x+12)=0


Domain of the equation: 6x+12)!=0

x∈R


We get rid of parentheses

3x+6/6x-12-6=0

We multiply all the terms by the denominator


3x*6x-12*6x-6*6x+6=0

Wy multiply elements

18x^2-72x-36x+6=0

We add all the numbers together, and all the variables

18x^2-108x+6=0

a = 18; b = -108; c = +6;
Δ = b2-4ac
Δ = -1082-4·18·6
Δ = 11232
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:

$\sqrt{\Delta}=\sqrt{11232}=\sqrt{144*78}=\sqrt{144}*\sqrt{78}=12\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-12\sqrt{78}}{2*18}=\frac{108-12\sqrt{78}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+12\sqrt{78}}{2*18}=\frac{108+12\sqrt{78}}{36}
$