2/x+3/2x=1/5

Solution for 2/x+3/2x=1/5 equation:

2/x+3/2x=1/5

We move all terms to the left:

2/x+3/2x-(1/5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+3/2x-(+1/5)=0

We get rid of parentheses

2/x+3/2x-1/5=0

We calculate fractions


(-4x^2)/50x^2+100x/50x^2+75x/50x^2=0

We multiply all the terms by the denominator


(-4x^2)+100x+75x=0

We add all the numbers together, and all the variables

(-4x^2)+175x=0

We get rid of parentheses

-4x^2+175x=0

a = -4; b = 175; c = 0;
Δ = b2-4ac
Δ = 1752-4·(-4)·0
Δ = 30625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30625}=175$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(175)-175}{2*-4}=\frac{-350}{-8}
=43+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(175)+175}{2*-4}=\frac{0}{-8}
=0
$