(8)/(3x)*6x=16

Solution for (8)/(3x)*6x=16 equation:

(8)/(3x)*6x=16

We move all terms to the left:

(8)/(3x)*6x-(16)=0


Domain of the equation: 3x*6x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-16*3x*6x+8=0

Wy multiply elements

-288x^2*6+8=0

Wy multiply elements

-1728x^2+8=0

a = -1728; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-1728)·8
Δ = 55296
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:

$\sqrt{\Delta}=\sqrt{55296}=\sqrt{9216*6}=\sqrt{9216}*\sqrt{6}=96\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96\sqrt{6}}{2*-1728}=\frac{0-96\sqrt{6}}{-3456}
=-\frac{96\sqrt{6}}{-3456}
=-\frac{\sqrt{6}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96\sqrt{6}}{2*-1728}=\frac{0+96\sqrt{6}}{-3456}
=\frac{96\sqrt{6}}{-3456}
=\frac{\sqrt{6}}{-36}
$