x+1/5x=590

Solution for x+1/5x=590 equation:

x+1/5x=590

We move all terms to the left:

x+1/5x-(590)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-590*5x+1=0

Wy multiply elements

5x^2-2950x+1=0

a = 5; b = -2950; c = +1;
Δ = b2-4ac
Δ = -29502-4·5·1
Δ = 8702480
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:

$\sqrt{\Delta}=\sqrt{8702480}=\sqrt{16*543905}=\sqrt{16}*\sqrt{543905}=4\sqrt{543905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2950)-4\sqrt{543905}}{2*5}=\frac{2950-4\sqrt{543905}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2950)+4\sqrt{543905}}{2*5}=\frac{2950+4\sqrt{543905}}{10}
$