120=4x+8/x

Solution for 120=4x+8/x equation:

120=4x+8/x

We move all terms to the left:

120-(4x+8/x)=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+8/x)+120=0

We get rid of parentheses

-4x-8/x+120=0

We multiply all the terms by the denominator


-4x*x+120*x-8=0

We add all the numbers together, and all the variables

120x-4x*x-8=0

Wy multiply elements

-4x^2+120x-8=0

a = -4; b = 120; c = -8;
Δ = b2-4ac
Δ = 1202-4·(-4)·(-8)
Δ = 14272
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:

$\sqrt{\Delta}=\sqrt{14272}=\sqrt{64*223}=\sqrt{64}*\sqrt{223}=8\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-8\sqrt{223}}{2*-4}=\frac{-120-8\sqrt{223}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+8\sqrt{223}}{2*-4}=\frac{-120+8\sqrt{223}}{-8}
$