3x-1/5x=2

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

3x-1/5x=2

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


3x*5x-2*5x-1=0

Wy multiply elements

15x^2-10x-1=0

a = 15; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·15·(-1)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{10}}{2*15}=\frac{10-4\sqrt{10}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{10}}{2*15}=\frac{10+4\sqrt{10}}{30}
$