x+1/5x=90

Solution for x+1/5x=90 equation:

x+1/5x=90

We move all terms to the left:

x+1/5x-(90)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-90*5x+1=0

Wy multiply elements

5x^2-450x+1=0

a = 5; b = -450; c = +1;
Δ = b2-4ac
Δ = -4502-4·5·1
Δ = 202480
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:

$\sqrt{\Delta}=\sqrt{202480}=\sqrt{16*12655}=\sqrt{16}*\sqrt{12655}=4\sqrt{12655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-4\sqrt{12655}}{2*5}=\frac{450-4\sqrt{12655}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+4\sqrt{12655}}{2*5}=\frac{450+4\sqrt{12655}}{10}
$