x+(1/7x)=19

Solution for x+(1/7x)=19 equation:

x+(1/7x)=19

We move all terms to the left:

x+(1/7x)-(19)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+1/7x)-19=0

We get rid of parentheses

x+1/7x-19=0

We multiply all the terms by the denominator


x*7x-19*7x+1=0

Wy multiply elements

7x^2-133x+1=0

a = 7; b = -133; c = +1;
Δ = b2-4ac
Δ = -1332-4·7·1
Δ = 17661
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:

$\sqrt{\Delta}=\sqrt{17661}=\sqrt{841*21}=\sqrt{841}*\sqrt{21}=29\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-133)-29\sqrt{21}}{2*7}=\frac{133-29\sqrt{21}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-133)+29\sqrt{21}}{2*7}=\frac{133+29\sqrt{21}}{14}
$