480=x*5*3x/2

Solution for 480=x*5*3x/2 equation:

480=x*5*3x/2

We move all terms to the left:

480-(x*5*3x/2)=0

We add all the numbers together, and all the variables

-(+x*5*3x/2)+480=0

We get rid of parentheses

-x*5*3x/2+480=0

We multiply all the terms by the denominator


-x*5*3x+480*2=0

We add all the numbers together, and all the variables

-x*5*3x+960=0

Wy multiply elements

-15x^2*3+960=0

Wy multiply elements

-45x^2+960=0

a = -45; b = 0; c = +960;
Δ = b2-4ac
Δ = 02-4·(-45)·960
Δ = 172800
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:

$\sqrt{\Delta}=\sqrt{172800}=\sqrt{57600*3}=\sqrt{57600}*\sqrt{3}=240\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-240\sqrt{3}}{2*-45}=\frac{0-240\sqrt{3}}{-90}
=-\frac{240\sqrt{3}}{-90}
=-\frac{8\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+240\sqrt{3}}{2*-45}=\frac{0+240\sqrt{3}}{-90}
=\frac{240\sqrt{3}}{-90}
=\frac{8\sqrt{3}}{-3}
$