6/x-1-3/7x-7=9

Solution for 6/x-1-3/7x-7=9 equation:

6/x-1-3/7x-7=9

We move all terms to the left:

6/x-1-3/7x-7-(9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

6/x-3/7x-17=0

We calculate fractions


42x/7x^2+(-3x)/7x^2-17=0

We multiply all the terms by the denominator


42x+(-3x)-17*7x^2=0

Wy multiply elements

-119x^2+42x+(-3x)=0

We get rid of parentheses

-119x^2+42x-3x=0

We add all the numbers together, and all the variables

-119x^2+39x=0

a = -119; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-119)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-119}=\frac{-78}{-238}
=39/119
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-119}=\frac{0}{-238}
=0
$