3/x-4/5x=1/10

Solution for 3/x-4/5x=1/10 equation:

3/x-4/5x=1/10

We move all terms to the left:

3/x-4/5x-(1/10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/x-4/5x-(+1/10)=0

We get rid of parentheses

3/x-4/5x-1/10=0

We calculate fractions


(-25x^2)/50x^2+150x/50x^2+(-40x)/50x^2=0

We multiply all the terms by the denominator


(-25x^2)+150x+(-40x)=0

We get rid of parentheses

-25x^2+150x-40x=0

We add all the numbers together, and all the variables

-25x^2+110x=0

a = -25; b = 110; c = 0;
Δ = b2-4ac
Δ = 1102-4·(-25)·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-110}{2*-25}=\frac{-220}{-50}
=4+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+110}{2*-25}=\frac{0}{-50}
=0
$