1/7x-x=84

Solution for 1/7x-x=84 equation:

1/7x-x=84

We move all terms to the left:

1/7x-x-(84)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/7x-84=0

We multiply all the terms by the denominator


-1x*7x-84*7x+1=0

Wy multiply elements

-7x^2-588x+1=0

a = -7; b = -588; c = +1;
Δ = b2-4ac
Δ = -5882-4·(-7)·1
Δ = 345772
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:

$\sqrt{\Delta}=\sqrt{345772}=\sqrt{4*86443}=\sqrt{4}*\sqrt{86443}=2\sqrt{86443}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-588)-2\sqrt{86443}}{2*-7}=\frac{588-2\sqrt{86443}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-588)+2\sqrt{86443}}{2*-7}=\frac{588+2\sqrt{86443}}{-14}
$