4x+80/x=320

Solution for 4x+80/x=320 equation:

4x+80/x=320

We move all terms to the left:

4x+80/x-(320)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-320*x+80=0

We add all the numbers together, and all the variables

-320x+4x*x+80=0

Wy multiply elements

4x^2-320x+80=0

a = 4; b = -320; c = +80;
Δ = b2-4ac
Δ = -3202-4·4·80
Δ = 101120
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:

$\sqrt{\Delta}=\sqrt{101120}=\sqrt{256*395}=\sqrt{256}*\sqrt{395}=16\sqrt{395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-16\sqrt{395}}{2*4}=\frac{320-16\sqrt{395}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+16\sqrt{395}}{2*4}=\frac{320+16\sqrt{395}}{8}
$