3x+2=1/4x

Solution for 3x+2=1/4x equation:

3x+2=1/4x

We move all terms to the left:

3x+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

3x-(+1/4x)+2=0

We get rid of parentheses

3x-1/4x+2=0

We multiply all the terms by the denominator


3x*4x+2*4x-1=0

Wy multiply elements

12x^2+8x-1=0

a = 12; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·12·(-1)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*12}=\frac{-8-4\sqrt{7}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*12}=\frac{-8+4\sqrt{7}}{24}
$