21n+39/12n=30

Solution for 21n+39/12n=30 equation:

21n+39/12n=30

We move all terms to the left:

21n+39/12n-(30)=0


Domain of the equation: 12n!=0

n!=0/12

n!=0

n∈R


We multiply all the terms by the denominator


21n*12n-30*12n+39=0

Wy multiply elements

252n^2-360n+39=0

a = 252; b = -360; c = +39;
Δ = b2-4ac
Δ = -3602-4·252·39
Δ = 90288
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:

$\sqrt{\Delta}=\sqrt{90288}=\sqrt{144*627}=\sqrt{144}*\sqrt{627}=12\sqrt{627}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-12\sqrt{627}}{2*252}=\frac{360-12\sqrt{627}}{504}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+12\sqrt{627}}{2*252}=\frac{360+12\sqrt{627}}{504}
$