9/2n=3n+12

Solution for 9/2n=3n+12 equation:

9/2n=3n+12

We move all terms to the left:

9/2n-(3n+12)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

9/2n-3n-12=0

We multiply all the terms by the denominator


-3n*2n-12*2n+9=0

Wy multiply elements

-6n^2-24n+9=0

a = -6; b = -24; c = +9;
Δ = b2-4ac
Δ = -242-4·(-6)·9
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{22}}{2*-6}=\frac{24-6\sqrt{22}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{22}}{2*-6}=\frac{24+6\sqrt{22}}{-12}
$