3/2(16n)+3=24n

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

3/2(16n)+3=24n

We move all terms to the left:

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

We multiply all the terms by the denominator


-24n*216n+3*216n+3=0

Wy multiply elements

-5184n^2+648n+3=0

a = -5184; b = 648; c = +3;
Δ = b2-4ac
Δ = 6482-4·(-5184)·3
Δ = 482112
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:

$\sqrt{\Delta}=\sqrt{482112}=\sqrt{5184*93}=\sqrt{5184}*\sqrt{93}=72\sqrt{93}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(648)-72\sqrt{93}}{2*-5184}=\frac{-648-72\sqrt{93}}{-10368}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(648)+72\sqrt{93}}{2*-5184}=\frac{-648+72\sqrt{93}}{-10368}
$