X=480/x-2

Solution for X=480/x-2 equation:

X=480/X-2

We move all terms to the left:

X-(480/X-2)=0


Domain of the equation: X-2)!=0

X∈R


We get rid of parentheses

X-480/X+2=0

We multiply all the terms by the denominator


X*X+2*X-480=0

We add all the numbers together, and all the variables

2X+X*X-480=0

Wy multiply elements

X^2+2X-480=0

a = 1; b = 2; c = -480;
Δ = b2-4ac
Δ = 22-4·1·(-480)
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{481}}{2*1}=\frac{-2-2\sqrt{481}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{481}}{2*1}=\frac{-2+2\sqrt{481}}{2}
$