4320/5x=3x

Solution for 4320/5x=3x equation:

4320/5x=3x

We move all terms to the left:

4320/5x-(3x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+4320/5x=0

We multiply all the terms by the denominator


-3x*5x+4320=0

Wy multiply elements

-15x^2+4320=0

a = -15; b = 0; c = +4320;
Δ = b2-4ac
Δ = 02-4·(-15)·4320
Δ = 259200
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:

$\sqrt{\Delta}=\sqrt{259200}=\sqrt{129600*2}=\sqrt{129600}*\sqrt{2}=360\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-360\sqrt{2}}{2*-15}=\frac{0-360\sqrt{2}}{-30}
=-\frac{360\sqrt{2}}{-30}
=-\frac{12\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+360\sqrt{2}}{2*-15}=\frac{0+360\sqrt{2}}{-30}
=\frac{360\sqrt{2}}{-30}
=\frac{12\sqrt{2}}{-1}
$