3200/x=3x

Solution for 3200/x=3x equation:

3200/x=3x

We move all terms to the left:

3200/x-(3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+3200/x=0

We multiply all the terms by the denominator


-3x*x+3200=0

Wy multiply elements

-3x^2+3200=0

a = -3; b = 0; c = +3200;
Δ = b2-4ac
Δ = 02-4·(-3)·3200
Δ = 38400
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:

$\sqrt{\Delta}=\sqrt{38400}=\sqrt{6400*6}=\sqrt{6400}*\sqrt{6}=80\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{6}}{2*-3}=\frac{0-80\sqrt{6}}{-6}
=-\frac{80\sqrt{6}}{-6}
=-\frac{40\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{6}}{2*-3}=\frac{0+80\sqrt{6}}{-6}
=\frac{80\sqrt{6}}{-6}
=\frac{40\sqrt{6}}{-3}
$