8/x=10/9x+1

Solution for 8/x=10/9x+1 equation:

8/x=10/9x+1

We move all terms to the left:

8/x-(10/9x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x+1)!=0

x∈R


We get rid of parentheses

8/x-10/9x-1=0

We calculate fractions


72x/9x^2+(-10x)/9x^2-1=0

We multiply all the terms by the denominator


72x+(-10x)-1*9x^2=0

Wy multiply elements

-9x^2+72x+(-10x)=0

We get rid of parentheses

-9x^2+72x-10x=0

We add all the numbers together, and all the variables

-9x^2+62x=0

a = -9; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·(-9)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*-9}=\frac{-124}{-18}
=6+8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*-9}=\frac{0}{-18}
=0
$