2/x=6/5x+4

Solution for 2/x=6/5x+4 equation:

2/x=6/5x+4

We move all terms to the left:

2/x-(6/5x+4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

2/x-6/5x-4=0

We calculate fractions


10x/5x^2+(-6x)/5x^2-4=0

We multiply all the terms by the denominator


10x+(-6x)-4*5x^2=0

Wy multiply elements

-20x^2+10x+(-6x)=0

We get rid of parentheses

-20x^2+10x-6x=0

We add all the numbers together, and all the variables

-20x^2+4x=0

a = -20; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-20)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-20}=\frac{-8}{-40}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-20}=\frac{0}{-40}
=0
$