3/2(16n)=24n

Solution for 3/2(16n)=24n equation:

3/2(16n)=24n

We move all terms to the left:

3/2(16n)-(24n)=0


Domain of the equation: 216n!=0

n!=0/216

n!=0

n∈R


We add all the numbers together, and all the variables

-24n+3/216n=0

We multiply all the terms by the denominator


-24n*216n+3=0

Wy multiply elements

-5184n^2+3=0

a = -5184; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-5184)·3
Δ = 62208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{62208}=\sqrt{20736*3}=\sqrt{20736}*\sqrt{3}=144\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{3}}{2*-5184}=\frac{0-144\sqrt{3}}{-10368}
=-\frac{144\sqrt{3}}{-10368}
=-\frac{\sqrt{3}}{-72}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{3}}{2*-5184}=\frac{0+144\sqrt{3}}{-10368}
=\frac{144\sqrt{3}}{-10368}
=\frac{\sqrt{3}}{-72}
$