X+1/5x=50

Solution for X+1/5x=50 equation:

X+1/5X=50

We move all terms to the left:

X+1/5X-(50)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-50*5X+1=0

Wy multiply elements

5X^2-250X+1=0

a = 5; b = -250; c = +1;
Δ = b2-4ac
Δ = -2502-4·5·1
Δ = 62480
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:

$\sqrt{\Delta}=\sqrt{62480}=\sqrt{16*3905}=\sqrt{16}*\sqrt{3905}=4\sqrt{3905}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-4\sqrt{3905}}{2*5}=\frac{250-4\sqrt{3905}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+4\sqrt{3905}}{2*5}=\frac{250+4\sqrt{3905}}{10}
$