2-3/4n=1/8n+9

Solution for 2-3/4n=1/8n+9 equation:

2-3/4n=1/8n+9

We move all terms to the left:

2-3/4n-(1/8n+9)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 8n+9)!=0

n∈R


We get rid of parentheses

-3/4n-1/8n-9+2=0

We calculate fractions


(-24n)/32n^2+(-4n)/32n^2-9+2=0

We add all the numbers together, and all the variables

(-24n)/32n^2+(-4n)/32n^2-7=0

We multiply all the terms by the denominator


(-24n)+(-4n)-7*32n^2=0

Wy multiply elements

-224n^2+(-24n)+(-4n)=0

We get rid of parentheses

-224n^2-24n-4n=0

We add all the numbers together, and all the variables

-224n^2-28n=0

a = -224; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-224)·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*-224}=\frac{0}{-448}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-224}=\frac{56}{-448}
=-1/8
$