x+x*1/x=10

Solution for x+x*1/x=10 equation:

x+x*1/x=10

We move all terms to the left:

x+x*1/x-(10)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x+x*1-10*x=0

We add all the numbers together, and all the variables

-10x+x*x+x*1=0

Wy multiply elements

x^2-10x+x=0

We add all the numbers together, and all the variables

x^2-9x=0

a = 1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·1·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*1}=\frac{18}{2}
=9
$