2x+1/5x=2

Solution for 2x+1/5x=2 equation:

2x+1/5x=2

We move all terms to the left:

2x+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


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

Wy multiply elements

10x^2-10x+1=0

a = 10; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·10·1
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{15}}{2*10}=\frac{10-2\sqrt{15}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{15}}{2*10}=\frac{10+2\sqrt{15}}{20}
$