7/8n-23/4=1/2n+3

Solution for 7/8n-23/4=1/2n+3 equation:

7/8n-23/4=1/2n+3

We move all terms to the left:

7/8n-23/4-(1/2n+3)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 2n+3)!=0

n∈R


We get rid of parentheses

7/8n-1/2n-3-23/4=0

We calculate fractions


(-736n^2)/256n^2+224n/256n^2+(-128n)/256n^2-3=0

We multiply all the terms by the denominator


(-736n^2)+224n+(-128n)-3*256n^2=0

Wy multiply elements

(-736n^2)-768n^2+224n+(-128n)=0

We get rid of parentheses

-736n^2-768n^2+224n-128n=0

We add all the numbers together, and all the variables

-1504n^2+96n=0

a = -1504; b = 96; c = 0;
Δ = b2-4ac
Δ = 962-4·(-1504)·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-96}{2*-1504}=\frac{-192}{-3008}
=3/47
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+96}{2*-1504}=\frac{0}{-3008}
=0
$