2/x+6/5x=3

Solution for 2/x+6/5x=3 equation:

2/x+6/5x=3

We move all terms to the left:

2/x+6/5x-(3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


10x/5x^2+6x/5x^2-3=0

We multiply all the terms by the denominator


10x+6x-3*5x^2=0

We add all the numbers together, and all the variables

16x-3*5x^2=0

Wy multiply elements

-15x^2+16x=0

a = -15; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-15)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-15}=\frac{-32}{-30}
=1+1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-15}=\frac{0}{-30}
=0
$