9x+1=8/x

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

9x+1=8/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

9x-8/x+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+9x*x-8=0

Wy multiply elements

9x^2+x-8=0

a = 9; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·9·(-8)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*9}=\frac{-18}{18}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*9}=\frac{16}{18}
=8/9
$