1/2x-8=1/9x

Solution for 1/2x-8=1/9x equation:

1/2x-8=1/9x

We move all terms to the left:

1/2x-8-(1/9x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+1/9x)-8=0

We get rid of parentheses

1/2x-1/9x-8=0

We calculate fractions


9x/18x^2+(-2x)/18x^2-8=0

We multiply all the terms by the denominator


9x+(-2x)-8*18x^2=0

Wy multiply elements

-144x^2+9x+(-2x)=0

We get rid of parentheses

-144x^2+9x-2x=0

We add all the numbers together, and all the variables

-144x^2+7x=0

a = -144; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-144)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-144}=\frac{-14}{-288}
=7/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-144}=\frac{0}{-288}
=0
$