2(1/4x-1)=2/3x+6

Solution for 2(1/4x-1)=2/3x+6 equation:

2(1/4x-1)=2/3x+6

We move all terms to the left:

2(1/4x-1)-(2/3x+6)=0


Domain of the equation: 4x-1)!=0

x∈R



Domain of the equation: 3x+6)!=0

x∈R


We multiply parentheses

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

We get rid of parentheses

2x-2/3x-6-2=0

We multiply all the terms by the denominator


2x*3x-6*3x-2*3x-2=0

Wy multiply elements

6x^2-18x-6x-2=0

We add all the numbers together, and all the variables

6x^2-24x-2=0

a = 6; b = -24; c = -2;
Δ = b2-4ac
Δ = -242-4·6·(-2)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*6}=\frac{24-4\sqrt{39}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*6}=\frac{24+4\sqrt{39}}{12}
$