X-(6-x)/9x-(7-x)=6

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

X-(6-X)/9X-(7-X)=6

We move all terms to the left:

X-(6-X)/9X-(7-X)-(6)=0


Domain of the equation: 9X!=0

X!=0/9

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


X*9X-(-1X+6)+1X*9X-7*9X-6*9X=0

Wy multiply elements

9X^2+9X^2-(-1X+6)-63X-54X=0

We get rid of parentheses

9X^2+9X^2+1X-63X-54X-6=0

We add all the numbers together, and all the variables

18X^2-116X-6=0

a = 18; b = -116; c = -6;
Δ = b2-4ac
Δ = -1162-4·18·(-6)
Δ = 13888
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:

$\sqrt{\Delta}=\sqrt{13888}=\sqrt{64*217}=\sqrt{64}*\sqrt{217}=8\sqrt{217}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-8\sqrt{217}}{2*18}=\frac{116-8\sqrt{217}}{36}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+8\sqrt{217}}{2*18}=\frac{116+8\sqrt{217}}{36}
$