x+1/5+x/2x=10

Solution for x+1/5+x/2x=10 equation:

x+1/5+x/2x=10

We move all terms to the left:

x+1/5+x/2x-(10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


determiningTheFunctionDomain
x+x/2x-10+1/5=0

We calculate fractions


x+5x/10x+2x/10x-10=0

We multiply all the terms by the denominator


x*10x+5x+2x-10*10x=0

We add all the numbers together, and all the variables

7x+x*10x-10*10x=0

Wy multiply elements

10x^2+7x-100x=0

We add all the numbers together, and all the variables

10x^2-93x=0

a = 10; b = -93; c = 0;
Δ = b2-4ac
Δ = -932-4·10·0
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-93)-93}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-93)+93}{2*10}=\frac{186}{20}
=9+3/10
$