11/12n-5/6n=9-5

Solution for 11/12n-5/6n=9-5 equation:

11/12n-5/6n=9-5

We move all terms to the left:

11/12n-5/6n-(9-5)=0


Domain of the equation: 12n!=0

n!=0/12

n!=0

n∈R



Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We add all the numbers together, and all the variables

11/12n-5/6n-4=0

We calculate fractions


66n/72n^2+(-60n)/72n^2-4=0

We multiply all the terms by the denominator


66n+(-60n)-4*72n^2=0

Wy multiply elements

-288n^2+66n+(-60n)=0

We get rid of parentheses

-288n^2+66n-60n=0

We add all the numbers together, and all the variables

-288n^2+6n=0

a = -288; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-288)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-288}=\frac{-12}{-576}
=1/48
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-288}=\frac{0}{-576}
=0
$