2/6x+8=4x-14

Solution for 2/6x+8=4x-14 equation:

2/6x+8=4x-14

We move all terms to the left:

2/6x+8-(4x-14)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

2/6x-4x+14+8=0

We multiply all the terms by the denominator


-4x*6x+14*6x+8*6x+2=0

Wy multiply elements

-24x^2+84x+48x+2=0

We add all the numbers together, and all the variables

-24x^2+132x+2=0

a = -24; b = 132; c = +2;
Δ = b2-4ac
Δ = 1322-4·(-24)·2
Δ = 17616
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:

$\sqrt{\Delta}=\sqrt{17616}=\sqrt{16*1101}=\sqrt{16}*\sqrt{1101}=4\sqrt{1101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-4\sqrt{1101}}{2*-24}=\frac{-132-4\sqrt{1101}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+4\sqrt{1101}}{2*-24}=\frac{-132+4\sqrt{1101}}{-48}
$