3x+7=1/3x+7

Solution for 3x+7=1/3x+7 equation:

3x+7=1/3x+7

We move all terms to the left:

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


Domain of the equation: 3x+7)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

9x^2-21x+21x-1=0

We add all the numbers together, and all the variables

9x^2-1=0

a = 9; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*9}=\frac{6}{18}
=1/3
$