1/2*3x*4x=96

Solution for 1/2*3x*4x=96 equation:

1/2*3x*4x=96

We move all terms to the left:

1/2*3x*4x-(96)=0


Domain of the equation: 2*3x*4x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-96*2*3x*4x+1=0

Wy multiply elements

-2304x^2*3+1=0

Wy multiply elements

-6912x^2+1=0

a = -6912; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-6912)·1
Δ = 27648
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:

$\sqrt{\Delta}=\sqrt{27648}=\sqrt{9216*3}=\sqrt{9216}*\sqrt{3}=96\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96\sqrt{3}}{2*-6912}=\frac{0-96\sqrt{3}}{-13824}
=-\frac{96\sqrt{3}}{-13824}
=-\frac{\sqrt{3}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96\sqrt{3}}{2*-6912}=\frac{0+96\sqrt{3}}{-13824}
=\frac{96\sqrt{3}}{-13824}
=\frac{\sqrt{3}}{-144}
$