7/8n-1/2=3/16n+5

Solution for 7/8n-1/2=3/16n+5 equation:

7/8n-1/2=3/16n+5

We move all terms to the left:

7/8n-1/2-(3/16n+5)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 16n+5)!=0

n∈R


We get rid of parentheses

7/8n-3/16n-5-1/2=0

We calculate fractions


(-128n^2)/512n^2+448n/512n^2+(-96n)/512n^2-5=0

We multiply all the terms by the denominator


(-128n^2)+448n+(-96n)-5*512n^2=0

Wy multiply elements

(-128n^2)-2560n^2+448n+(-96n)=0

We get rid of parentheses

-128n^2-2560n^2+448n-96n=0

We add all the numbers together, and all the variables

-2688n^2+352n=0

a = -2688; b = 352; c = 0;
Δ = b2-4ac
Δ = 3522-4·(-2688)·0
Δ = 123904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{123904}=352$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(352)-352}{2*-2688}=\frac{-704}{-5376}
=11/84
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(352)+352}{2*-2688}=\frac{0}{-5376}
=0
$