(3x+7)/6x+1/x=1

Solution for (3x+7)/6x+1/x=1 equation:

(3x+7)/6x+1/x=1

We move all terms to the left:

(3x+7)/6x+1/x-(1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


(3x^2+7x)/6x^2+6x/6x^2-1=0

We multiply all the terms by the denominator


(3x^2+7x)+6x-1*6x^2=0

We add all the numbers together, and all the variables

6x+(3x^2+7x)-1*6x^2=0

Wy multiply elements

-6x^2+6x+(3x^2+7x)=0

We get rid of parentheses

-6x^2+3x^2+6x+7x=0

We add all the numbers together, and all the variables

-3x^2+13x=0

a = -3; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-3)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-3}=\frac{-26}{-6}
=4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-3}=\frac{0}{-6}
=0
$