(x+2)(480/x-8)=480

Solution for (x+2)(480/x-8)=480 equation:

(x+2)(480/x-8)=480

We move all terms to the left:

(x+2)(480/x-8)-(480)=0


Domain of the equation: x-8)!=0

x∈R


We multiply parentheses ..

(+480x^2-8x+960x-16)-480=0

We get rid of parentheses

480x^2-8x+960x-16-480=0

We add all the numbers together, and all the variables

480x^2+952x-496=0

a = 480; b = 952; c = -496;
Δ = b2-4ac
Δ = 9522-4·480·(-496)
Δ = 1858624
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:

$\sqrt{\Delta}=\sqrt{1858624}=\sqrt{64*29041}=\sqrt{64}*\sqrt{29041}=8\sqrt{29041}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(952)-8\sqrt{29041}}{2*480}=\frac{-952-8\sqrt{29041}}{960}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(952)+8\sqrt{29041}}{2*480}=\frac{-952+8\sqrt{29041}}{960}
$