(1/7x)+x-6=0

Solution for (1/7x)+x-6=0 equation:

(1/7x)+x-6=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/7x)+x-6=0

We add all the numbers together, and all the variables

x+(+1/7x)-6=0

We get rid of parentheses

x+1/7x-6=0

We multiply all the terms by the denominator


x*7x-6*7x+1=0

Wy multiply elements

7x^2-42x+1=0

a = 7; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·7·1
Δ = 1736
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:

$\sqrt{\Delta}=\sqrt{1736}=\sqrt{4*434}=\sqrt{4}*\sqrt{434}=2\sqrt{434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{434}}{2*7}=\frac{42-2\sqrt{434}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{434}}{2*7}=\frac{42+2\sqrt{434}}{14}
$