21=x+1/5x

Solution for 21=x+1/5x equation:

21=x+1/5x

We move all terms to the left:

21-(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)+21=0

We get rid of parentheses

-x-1/5x+21=0

We multiply all the terms by the denominator


-x*5x+21*5x-1=0

Wy multiply elements

-5x^2+105x-1=0

a = -5; b = 105; c = -1;
Δ = b2-4ac
Δ = 1052-4·(-5)·(-1)
Δ = 11005
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-\sqrt{11005}}{2*-5}=\frac{-105-\sqrt{11005}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11005}}{2*-5}=\frac{-105+\sqrt{11005}}{-10}
$