x-8=480/2x

Solution for x-8=480/2x equation:

x-8=480/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-480/2x-8=0

We multiply all the terms by the denominator


x*2x-8*2x-480=0

Wy multiply elements

2x^2-16x-480=0

a = 2; b = -16; c = -480;
Δ = b2-4ac
Δ = -162-4·2·(-480)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-64}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+64}{2*2}=\frac{80}{4}
=20
$