1/X-2/5=3/2x

Solution for 1/X-2/5=3/2x equation:

1/X-2/5=3/2X

We move all terms to the left:

1/X-2/5-(3/2X)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/X-3/2X-2/5=0

We calculate fractions


(-8X^2)/50X^2+50X/50X^2+(-75X)/50X^2=0

We multiply all the terms by the denominator


(-8X^2)+50X+(-75X)=0

We get rid of parentheses

-8X^2+50X-75X=0

We add all the numbers together, and all the variables

-8X^2-25X=0

a = -8; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-8)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-8}=\frac{0}{-16}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-8}=\frac{50}{-16}
=-3+1/8
$