3/x=6/7x+6

Solution for 3/x=6/7x+6 equation:

3/x=6/7x+6

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x+6)!=0

x∈R


We get rid of parentheses

3/x-6/7x-6=0

We calculate fractions


21x/7x^2+(-6x)/7x^2-6=0

We multiply all the terms by the denominator


21x+(-6x)-6*7x^2=0

Wy multiply elements

-42x^2+21x+(-6x)=0

We get rid of parentheses

-42x^2+21x-6x=0

We add all the numbers together, and all the variables

-42x^2+15x=0

a = -42; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-42)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-42}=\frac{-30}{-84}
=5/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-42}=\frac{0}{-84}
=0
$