X+1/5x=20

Solution for X+1/5x=20 equation:

X+1/5X=20

We move all terms to the left:

X+1/5X-(20)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-20*5X+1=0

Wy multiply elements

5X^2-100X+1=0

a = 5; b = -100; c = +1;
Δ = b2-4ac
Δ = -1002-4·5·1
Δ = 9980
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:

$\sqrt{\Delta}=\sqrt{9980}=\sqrt{4*2495}=\sqrt{4}*\sqrt{2495}=2\sqrt{2495}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2495}}{2*5}=\frac{100-2\sqrt{2495}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2495}}{2*5}=\frac{100+2\sqrt{2495}}{10}
$