4x+(48/x)=80

Solution for 4x+(48/x)=80 equation:

4x+(48/x)=80

We move all terms to the left:

4x+(48/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

4x+(+48/x)-80=0

We get rid of parentheses

4x+48/x-80=0

We multiply all the terms by the denominator


4x*x-80*x+48=0

We add all the numbers together, and all the variables

-80x+4x*x+48=0

Wy multiply elements

4x^2-80x+48=0

a = 4; b = -80; c = +48;
Δ = b2-4ac
Δ = -802-4·4·48
Δ = 5632
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:

$\sqrt{\Delta}=\sqrt{5632}=\sqrt{256*22}=\sqrt{256}*\sqrt{22}=16\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{22}}{2*4}=\frac{80-16\sqrt{22}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{22}}{2*4}=\frac{80+16\sqrt{22}}{8}
$