2=21n+13/12n+15

Solution for 2=21n+13/12n+15 equation:

2=21n+13/12n+15

We move all terms to the left:

2-(21n+13/12n+15)=0


Domain of the equation: 12n+15)!=0

n∈R


We get rid of parentheses

-21n-13/12n-15+2=0

We multiply all the terms by the denominator


-21n*12n-15*12n+2*12n-13=0

Wy multiply elements

-252n^2-180n+24n-13=0

We add all the numbers together, and all the variables

-252n^2-156n-13=0

a = -252; b = -156; c = -13;
Δ = b2-4ac
Δ = -1562-4·(-252)·(-13)
Δ = 11232
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:

$\sqrt{\Delta}=\sqrt{11232}=\sqrt{144*78}=\sqrt{144}*\sqrt{78}=12\sqrt{78}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-12\sqrt{78}}{2*-252}=\frac{156-12\sqrt{78}}{-504}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+12\sqrt{78}}{2*-252}=\frac{156+12\sqrt{78}}{-504}
$