x+1/5x=21

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

x+1/5x=21

We move all terms to the left:

x+1/5x-(21)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


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}
$