2x+28=4/6x

Solution for 2x+28=4/6x equation:

2x+28=4/6x

We move all terms to the left:

2x+28-(4/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+4/6x)+28=0

We get rid of parentheses

2x-4/6x+28=0

We multiply all the terms by the denominator


2x*6x+28*6x-4=0

Wy multiply elements

12x^2+168x-4=0

a = 12; b = 168; c = -4;
Δ = b2-4ac
Δ = 1682-4·12·(-4)
Δ = 28416
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:

$\sqrt{\Delta}=\sqrt{28416}=\sqrt{256*111}=\sqrt{256}*\sqrt{111}=16\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-16\sqrt{111}}{2*12}=\frac{-168-16\sqrt{111}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+16\sqrt{111}}{2*12}=\frac{-168+16\sqrt{111}}{24}
$