(40/x)+x=80

Solution for (40/x)+x=80 equation:

(40/x)+x=80

We move all terms to the left:

(40/x)+x-(80)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+40/x)+x-80=0

We add all the numbers together, and all the variables

x+(+40/x)-80=0

We get rid of parentheses

x+40/x-80=0

We multiply all the terms by the denominator


x*x-80*x+40=0

We add all the numbers together, and all the variables

-80x+x*x+40=0

Wy multiply elements

x^2-80x+40=0

a = 1; b = -80; c = +40;
Δ = b2-4ac
Δ = -802-4·1·40
Δ = 6240
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:

$\sqrt{\Delta}=\sqrt{6240}=\sqrt{16*390}=\sqrt{16}*\sqrt{390}=4\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{390}}{2*1}=\frac{80-4\sqrt{390}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{390}}{2*1}=\frac{80+4\sqrt{390}}{2}
$