(x/x-9)+(x-6/7x+9)=1

Solution for (x/x-9)+(x-6/7x+9)=1 equation:

(x/x-9)+(x-6/7x+9)=1

We move all terms to the left:

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


Domain of the equation: x-9)!=0

x∈R



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

x∈R


We get rid of parentheses

x/x+x-6/7x-9+9-1=0

Fractions to decimals

-6/7x+x-9+9-1+1=0

We multiply all the terms by the denominator


x*7x-9*7x+9*7x-1*7x+1*7x-6=0

Wy multiply elements

7x^2-63x+63x-7x+7x-6=0

We add all the numbers together, and all the variables

7x^2-6=0

a = 7; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·7·(-6)
Δ = 168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*7}=\frac{0-2\sqrt{42}}{14}
=-\frac{2\sqrt{42}}{14}
=-\frac{\sqrt{42}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*7}=\frac{0+2\sqrt{42}}{14}
=\frac{2\sqrt{42}}{14}
=\frac{\sqrt{42}}{7}
$