8/x=8+4/9x

Solution for 8/x=8+4/9x equation:

8/x=8+4/9x

We move all terms to the left:

8/x-(8+4/9x)=0


Domain of the equation: 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

8/x-(4/9x+8)=0

We get rid of parentheses

8/x-4/9x-8=0

We calculate fractions


72x/9x^2+(-4x)/9x^2-8=0

We multiply all the terms by the denominator


72x+(-4x)-8*9x^2=0

Wy multiply elements

-72x^2+72x+(-4x)=0

We get rid of parentheses

-72x^2+72x-4x=0

We add all the numbers together, and all the variables

-72x^2+68x=0

a = -72; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-72)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-72}=\frac{-136}{-144}
=17/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-72}=\frac{0}{-144}
=0
$