480=x-1/4x

Solution for 480=x-1/4x equation:

480=x-1/4x

We move all terms to the left:

480-(x-1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x-1/4x)+480=0

We get rid of parentheses

-x+1/4x+480=0

We multiply all the terms by the denominator


-x*4x+480*4x+1=0

Wy multiply elements

-4x^2+1920x+1=0

a = -4; b = 1920; c = +1;
Δ = b2-4ac
Δ = 19202-4·(-4)·1
Δ = 3686416
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:

$\sqrt{\Delta}=\sqrt{3686416}=\sqrt{16*230401}=\sqrt{16}*\sqrt{230401}=4\sqrt{230401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1920)-4\sqrt{230401}}{2*-4}=\frac{-1920-4\sqrt{230401}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1920)+4\sqrt{230401}}{2*-4}=\frac{-1920+4\sqrt{230401}}{-8}
$