x+1/5x=2160

Solution for x+1/5x=2160 equation:

x+1/5x=2160

We move all terms to the left:

x+1/5x-(2160)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-2160*5x+1=0

Wy multiply elements

5x^2-10800x+1=0

a = 5; b = -10800; c = +1;
Δ = b2-4ac
Δ = -108002-4·5·1
Δ = 116639980
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:

$\sqrt{\Delta}=\sqrt{116639980}=\sqrt{4*29159995}=\sqrt{4}*\sqrt{29159995}=2\sqrt{29159995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10800)-2\sqrt{29159995}}{2*5}=\frac{10800-2\sqrt{29159995}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10800)+2\sqrt{29159995}}{2*5}=\frac{10800+2\sqrt{29159995}}{10}
$