3x-1=14/2x

Solution for 3x-1=14/2x equation:

3x-1=14/2x

We move all terms to the left:

3x-1-(14/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+14/2x)-1=0

We get rid of parentheses

3x-14/2x-1=0

We multiply all the terms by the denominator


3x*2x-1*2x-14=0

Wy multiply elements

6x^2-2x-14=0

a = 6; b = -2; c = -14;
Δ = b2-4ac
Δ = -22-4·6·(-14)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{85}}{2*6}=\frac{2-2\sqrt{85}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{85}}{2*6}=\frac{2+2\sqrt{85}}{12}
$