X+1/5x=2

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

X+1/5X=2

We move all terms to the left:

X+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


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

Wy multiply elements

5X^2-10X+1=0

a = 5; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·5·1
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{5}}{2*5}=\frac{10-4\sqrt{5}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{5}}{2*5}=\frac{10+4\sqrt{5}}{10}
$