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

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

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

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


15x/5x^2+4x/5x^2-2=0

We multiply all the terms by the denominator


15x+4x-2*5x^2=0

We add all the numbers together, and all the variables

19x-2*5x^2=0

Wy multiply elements

-10x^2+19x=0

a = -10; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-10)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-10}=\frac{-38}{-20}
=1+9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-10}=\frac{0}{-20}
=0
$