6/x=9/7x+9

Solution for 6/x=9/7x+9 equation:

6/x=9/7x+9

We move all terms to the left:

6/x-(9/7x+9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x+9)!=0

x∈R


We get rid of parentheses

6/x-9/7x-9=0

We calculate fractions


42x/7x^2+(-9x)/7x^2-9=0

We multiply all the terms by the denominator


42x+(-9x)-9*7x^2=0

Wy multiply elements

-63x^2+42x+(-9x)=0

We get rid of parentheses

-63x^2+42x-9x=0

We add all the numbers together, and all the variables

-63x^2+33x=0

a = -63; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-63)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-63}=\frac{-66}{-126}
=11/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-63}=\frac{0}{-126}
=0
$