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

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

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

We move all terms to the left:

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


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

x∈R


We multiply parentheses ..

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

We get rid of parentheses

480x^2+3x-3840x-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}
$