3x/3x+7-3x+7/3x=14

Solution for 3x/3x+7-3x+7/3x=14 equation:

3x/3x+7-3x+7/3x=14

We move all terms to the left:

3x/3x+7-3x+7/3x-(14)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+3x/3x+7/3x-7=0

Fractions to decimals

7/3x-3x-7+1=0

We multiply all the terms by the denominator


-3x*3x-7*3x+1*3x+7=0

Wy multiply elements

-9x^2-21x+3x+7=0

We add all the numbers together, and all the variables

-9x^2-18x+7=0

a = -9; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·(-9)·7
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-24}{2*-9}=\frac{-6}{-18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+24}{2*-9}=\frac{42}{-18}
=-2+1/3
$