2/3x+6=4x-12

Solution for 2/3x+6=4x-12 equation:

2/3x+6=4x-12

We move all terms to the left:

2/3x+6-(4x-12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-4x+12+6=0

We multiply all the terms by the denominator


-4x*3x+12*3x+6*3x+2=0

Wy multiply elements

-12x^2+36x+18x+2=0

We add all the numbers together, and all the variables

-12x^2+54x+2=0

a = -12; b = 54; c = +2;
Δ = b2-4ac
Δ = 542-4·(-12)·2
Δ = 3012
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:

$\sqrt{\Delta}=\sqrt{3012}=\sqrt{4*753}=\sqrt{4}*\sqrt{753}=2\sqrt{753}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{753}}{2*-12}=\frac{-54-2\sqrt{753}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{753}}{2*-12}=\frac{-54+2\sqrt{753}}{-24}
$