24x*42x=1/16

Solution for 24x*42x=1/16 equation:

24x*42x=1/16

We move all terms to the left:

24x*42x-(1/16)=0

We add all the numbers together, and all the variables

24x*42x-(+1/16)=0

Wy multiply elements

1008x^2-(+1/16)=0

We get rid of parentheses

1008x^2-1/16=0

We multiply all the terms by the denominator


1008x^2*16-1=0

Wy multiply elements

16128x^2-1=0

a = 16128; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·16128·(-1)
Δ = 64512
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:

$\sqrt{\Delta}=\sqrt{64512}=\sqrt{9216*7}=\sqrt{9216}*\sqrt{7}=96\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96\sqrt{7}}{2*16128}=\frac{0-96\sqrt{7}}{32256}
=-\frac{96\sqrt{7}}{32256}
=-\frac{\sqrt{7}}{336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96\sqrt{7}}{2*16128}=\frac{0+96\sqrt{7}}{32256}
=\frac{96\sqrt{7}}{32256}
=\frac{\sqrt{7}}{336}
$