84=x-1/5x

Solution for 84=x-1/5x equation:

84=x-1/5x

We move all terms to the left:

84-(x-1/5x)=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}
$