3/4n+1/8n-6=15

Solution for 3/4n+1/8n-6=15 equation:

3/4n+1/8n-6=15

We move all terms to the left:

3/4n+1/8n-6-(15)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R


We add all the numbers together, and all the variables

3/4n+1/8n-21=0

We calculate fractions


24n/32n^2+4n/32n^2-21=0

We multiply all the terms by the denominator


24n+4n-21*32n^2=0

We add all the numbers together, and all the variables

28n-21*32n^2=0

Wy multiply elements

-672n^2+28n=0

a = -672; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-672)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-672}=\frac{-56}{-1344}
=1/24
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-672}=\frac{0}{-1344}
=0
$