1/2n-2/3n-3/8=-11/8

Solution for 1/2n-2/3n-3/8=-11/8 equation:

1/2n-2/3n-3/8=-11/8

We move all terms to the left:

1/2n-2/3n-3/8-(-11/8)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

1/2n-2/3n-3/8+11/8=0

We calculate fractions


192n/384n^2+(-256n)/384n^2+(198n^2-3)/384n^2=0

We multiply all the terms by the denominator


192n+(-256n)+(198n^2-3)=0

We get rid of parentheses

198n^2+192n-256n-3=0

We add all the numbers together, and all the variables

198n^2-64n-3=0

a = 198; b = -64; c = -3;
Δ = b2-4ac
Δ = -642-4·198·(-3)
Δ = 6472
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:

$\sqrt{\Delta}=\sqrt{6472}=\sqrt{4*1618}=\sqrt{4}*\sqrt{1618}=2\sqrt{1618}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-2\sqrt{1618}}{2*198}=\frac{64-2\sqrt{1618}}{396}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+2\sqrt{1618}}{2*198}=\frac{64+2\sqrt{1618}}{396}
$