9x-10=9/x

Solution for 9x-10=9/x equation:

9x-10=9/x

We move all terms to the left:

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

We get rid of parentheses

9x-9/x-10=0

We multiply all the terms by the denominator


9x*x-10*x-9=0

We add all the numbers together, and all the variables

-10x+9x*x-9=0

Wy multiply elements

9x^2-10x-9=0

a = 9; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·9·(-9)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{106}}{2*9}=\frac{10-2\sqrt{106}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{106}}{2*9}=\frac{10+2\sqrt{106}}{18}
$