480=(x-8)(480/x+3)

Solution for 480=(x-8)(480/x+3) equation:

480=(x-8)(480/x+3)

We move all terms to the left:

480-((x-8)(480/x+3))=0


Domain of the equation: x+3))!=0

x∈R


We multiply parentheses ..

-((+480x^2+3x-3840x-24))+480=0


We calculate terms in parentheses: -((+480x^2+3x-3840x-24)), so:

(+480x^2+3x-3840x-24)

We get rid of parentheses

480x^2+3x-3840x-24

We add all the numbers together, and all the variables

480x^2-3837x-24

Back to the equation:

-(480x^2-3837x-24)


We get rid of parentheses

-480x^2+3837x+24+480=0

We add all the numbers together, and all the variables

-480x^2+3837x+504=0

a = -480; b = 3837; c = +504;
Δ = b2-4ac
Δ = 38372-4·(-480)·504
Δ = 15690249
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:

$\sqrt{\Delta}=\sqrt{15690249}=\sqrt{9*1743361}=\sqrt{9}*\sqrt{1743361}=3\sqrt{1743361}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3837)-3\sqrt{1743361}}{2*-480}=\frac{-3837-3\sqrt{1743361}}{-960}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3837)+3\sqrt{1743361}}{2*-480}=\frac{-3837+3\sqrt{1743361}}{-960}
$