85/x+5x=90

Solution for 85/x+5x=90 equation:

85/x+5x=90

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x+85/x-90=0

We multiply all the terms by the denominator


5x*x-90*x+85=0

We add all the numbers together, and all the variables

-90x+5x*x+85=0

Wy multiply elements

5x^2-90x+85=0

a = 5; b = -90; c = +85;
Δ = b2-4ac
Δ = -902-4·5·85
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-80}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+80}{2*5}=\frac{170}{10}
=17
$