480=(480/x-20)*(x+4)

Solution for 480=(480/x-20)*(x+4) equation:

480=(480/x-20)(x+4)

We move all terms to the left:

480-((480/x-20)(x+4))=0


Domain of the equation: x-20)(x+4))!=0

x∈R


We multiply parentheses ..

-((+480x^2+1920x-20x-80))+480=0


We calculate terms in parentheses: -((+480x^2+1920x-20x-80)), so:

(+480x^2+1920x-20x-80)

We get rid of parentheses

480x^2+1920x-20x-80

We add all the numbers together, and all the variables

480x^2+1900x-80

Back to the equation:

-(480x^2+1900x-80)


We get rid of parentheses

-480x^2-1900x+80+480=0

We add all the numbers together, and all the variables

-480x^2-1900x+560=0

a = -480; b = -1900; c = +560;
Δ = b2-4ac
Δ = -19002-4·(-480)·560
Δ = 4685200
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:

$\sqrt{\Delta}=\sqrt{4685200}=\sqrt{400*11713}=\sqrt{400}*\sqrt{11713}=20\sqrt{11713}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1900)-20\sqrt{11713}}{2*-480}=\frac{1900-20\sqrt{11713}}{-960}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1900)+20\sqrt{11713}}{2*-480}=\frac{1900+20\sqrt{11713}}{-960}
$