2/6x+4=4x-8

Solution for 2/6x+4=4x-8 equation:

2/6x+4=4x-8

We move all terms to the left:

2/6x+4-(4x-8)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

2/6x-4x+8+4=0

We multiply all the terms by the denominator


-4x*6x+8*6x+4*6x+2=0

Wy multiply elements

-24x^2+48x+24x+2=0

We add all the numbers together, and all the variables

-24x^2+72x+2=0

a = -24; b = 72; c = +2;
Δ = b2-4ac
Δ = 722-4·(-24)·2
Δ = 5376
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:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-16\sqrt{21}}{2*-24}=\frac{-72-16\sqrt{21}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+16\sqrt{21}}{2*-24}=\frac{-72+16\sqrt{21}}{-48}
$