4/8n-8-1/3n=7

Solution for 4/8n-8-1/3n=7 equation:

4/8n-8-1/3n=7

We move all terms to the left:

4/8n-8-1/3n-(7)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

4/8n-1/3n-15=0

We calculate fractions


12n/24n^2+(-8n)/24n^2-15=0

We multiply all the terms by the denominator


12n+(-8n)-15*24n^2=0

Wy multiply elements

-360n^2+12n+(-8n)=0

We get rid of parentheses

-360n^2+12n-8n=0

We add all the numbers together, and all the variables

-360n^2+4n=0

a = -360; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-360)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-360}=\frac{-8}{-720}
=1/90
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-360}=\frac{0}{-720}
=0
$