1/10+2/x=16/5x

Solution for 1/10+2/x=16/5x equation:

1/10+2/x=16/5x

We move all terms to the left:

1/10+2/x-(16/5x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/x-(+16/5x)+1/10=0

We get rid of parentheses

2/x-16/5x+1/10=0

We calculate fractions


25x^2/50x^2+100x/50x^2+(-160x)/50x^2=0

We multiply all the terms by the denominator


25x^2+100x+(-160x)=0

We get rid of parentheses

25x^2+100x-160x=0

We add all the numbers together, and all the variables

25x^2-60x=0

a = 25; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·25·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*25}=\frac{0}{50}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*25}=\frac{120}{50}
=2+2/5
$