6x+2=1/4x

Solution for 6x+2=1/4x equation:

6x+2=1/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

6x-1/4x+2=0

We multiply all the terms by the denominator


6x*4x+2*4x-1=0

Wy multiply elements

24x^2+8x-1=0

a = 24; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·24·(-1)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*24}=\frac{-8-4\sqrt{10}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*24}=\frac{-8+4\sqrt{10}}{48}
$