3x*(192/x+2x)=960

Solution for 3x*(192/x+2x)=960 equation:

3x(192/x+2x)=960

We move all terms to the left:

3x(192/x+2x)-(960)=0


Domain of the equation: x+2x)!=0

x∈R


We add all the numbers together, and all the variables

3x(+2x+192/x)-960=0

We multiply parentheses

6x^2+576x^2-960=0

We add all the numbers together, and all the variables

582x^2-960=0

a = 582; b = 0; c = -960;
Δ = b2-4ac
Δ = 02-4·582·(-960)
Δ = 2234880
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:

$\sqrt{\Delta}=\sqrt{2234880}=\sqrt{2304*970}=\sqrt{2304}*\sqrt{970}=48\sqrt{970}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{970}}{2*582}=\frac{0-48\sqrt{970}}{1164}
=-\frac{48\sqrt{970}}{1164}
=-\frac{4\sqrt{970}}{97}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{970}}{2*582}=\frac{0+48\sqrt{970}}{1164}
=\frac{48\sqrt{970}}{1164}
=\frac{4\sqrt{970}}{97}
$