10=x+9/x

Solution for 10=x+9/x equation:

10=x+9/x

We move all terms to the left:

10-(x+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

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

We get rid of parentheses

-x-9/x+10=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

10x-x*x-9=0

Wy multiply elements

-1x^2+10x-9=0

a = -1; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·(-1)·(-9)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8}{2*-1}=\frac{-2}{-2}
=1
$