2x+4=2/3x-4

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

2x+4=2/3x-4

We move all terms to the left:

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


Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+12x+12x-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}
$