2x+14/3x=1+3x

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

2x+14/3x=1+3x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-9x^2-3x+14=0

We add all the numbers together, and all the variables

-3x^2-3x+14=0

a = -3; b = -3; c = +14;
Δ = b2-4ac
Δ = -32-4·(-3)·14
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{177}}{2*-3}=\frac{3-\sqrt{177}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{177}}{2*-3}=\frac{3+\sqrt{177}}{-6}
$