1/6x-9=1x+8

Solution for 1/6x-9=1x+8 equation:

1/6x-9=1x+8

We move all terms to the left:

1/6x-9-(1x+8)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/6x-(x+8)-9=0

We get rid of parentheses

1/6x-x-8-9=0

We multiply all the terms by the denominator


-x*6x-8*6x-9*6x+1=0

Wy multiply elements

-6x^2-48x-54x+1=0

We add all the numbers together, and all the variables

-6x^2-102x+1=0

a = -6; b = -102; c = +1;
Δ = b2-4ac
Δ = -1022-4·(-6)·1
Δ = 10428
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:

$\sqrt{\Delta}=\sqrt{10428}=\sqrt{4*2607}=\sqrt{4}*\sqrt{2607}=2\sqrt{2607}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{2607}}{2*-6}=\frac{102-2\sqrt{2607}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{2607}}{2*-6}=\frac{102+2\sqrt{2607}}{-12}
$