480/x=2x

Solution for 480/x=2x equation:

480/x=2x

We move all terms to the left:

480/x-(2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x+480/x=0

We multiply all the terms by the denominator


-2x*x+480=0

Wy multiply elements

-2x^2+480=0

a = -2; b = 0; c = +480;
Δ = b2-4ac
Δ = 02-4·(-2)·480
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*-2}=\frac{0-16\sqrt{15}}{-4}
=-\frac{16\sqrt{15}}{-4}
=-\frac{4\sqrt{15}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*-2}=\frac{0+16\sqrt{15}}{-4}
=\frac{16\sqrt{15}}{-4}
=\frac{4\sqrt{15}}{-1}
$