X-1/7x=84

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

X-1/7X=84

We move all terms to the left:

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


Domain of the equation: 7X!=0

X!=0/7

X!=0

X∈R


We multiply all the terms by the denominator


X*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}
$