(X)-(1/5x)=84

Solution for (X)-(1/5x)=84 equation:

(X)-(1/5X)=84

We move all terms to the left:

(X)-(1/5X)-(84)=0


Domain of the equation: 5X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1/5X)-84=0

We get rid of parentheses

X-1/5X-84=0

We multiply all the terms by the denominator


X*5X-84*5X-1=0

Wy multiply elements

5X^2-420X-1=0

a = 5; b = -420; c = -1;
Δ = b2-4ac
Δ = -4202-4·5·(-1)
Δ = 176420
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:

$\sqrt{\Delta}=\sqrt{176420}=\sqrt{4*44105}=\sqrt{4}*\sqrt{44105}=2\sqrt{44105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-2\sqrt{44105}}{2*5}=\frac{420-2\sqrt{44105}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+2\sqrt{44105}}{2*5}=\frac{420+2\sqrt{44105}}{10}
$