x+(1/5x)=195

Solution for x+(1/5x)=195 equation:

x+(1/5x)=195

We move all terms to the left:

x+(1/5x)-(195)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+1/5x)-195=0

We get rid of parentheses

x+1/5x-195=0

We multiply all the terms by the denominator


x*5x-195*5x+1=0

Wy multiply elements

5x^2-975x+1=0

a = 5; b = -975; c = +1;
Δ = b2-4ac
Δ = -9752-4·5·1
Δ = 950605
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-975)-\sqrt{950605}}{2*5}=\frac{975-\sqrt{950605}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-975)+\sqrt{950605}}{2*5}=\frac{975+\sqrt{950605}}{10}
$