85/x+5x=80

Solution for 85/x+5x=80 equation:

85/x+5x=80

We move all terms to the left:

85/x+5x-(80)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x+85/x-80=0

We multiply all the terms by the denominator


5x*x-80*x+85=0

We add all the numbers together, and all the variables

-80x+5x*x+85=0

Wy multiply elements

5x^2-80x+85=0

a = 5; b = -80; c = +85;
Δ = b2-4ac
Δ = -802-4·5·85
Δ = 4700
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:

$\sqrt{\Delta}=\sqrt{4700}=\sqrt{100*47}=\sqrt{100}*\sqrt{47}=10\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-10\sqrt{47}}{2*5}=\frac{80-10\sqrt{47}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+10\sqrt{47}}{2*5}=\frac{80+10\sqrt{47}}{10}
$