4/5+4/x=3/2x

Solution for 4/5+4/x=3/2x equation:

4/5+4/x=3/2x

We move all terms to the left:

4/5+4/x-(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

4/x-(+3/2x)+4/5=0

We get rid of parentheses

4/x-3/2x+4/5=0

We calculate fractions


16x^2/50x^2+200x/50x^2+(-75x)/50x^2=0

We multiply all the terms by the denominator


16x^2+200x+(-75x)=0

We get rid of parentheses

16x^2+200x-75x=0

We add all the numbers together, and all the variables

16x^2+125x=0

a = 16; b = 125; c = 0;
Δ = b2-4ac
Δ = 1252-4·16·0
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125}{2*16}=\frac{-250}{32}
=-7+13/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125}{2*16}=\frac{0}{32}
=0
$