1/7x-x=84

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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} $

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