.750n+16=2-1/8n

Solution for .750n+16=2-1/8n equation:

.750n+16=2-1/8n

We move all terms to the left:

.750n+16-(2-1/8n)=0


Domain of the equation: 8n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

.750n-(-1/8n+2)+16=0

We get rid of parentheses

.750n+1/8n-2+16=0

We multiply all the terms by the denominator


(.750n)*8n-2*8n+16*8n+1=0

We add all the numbers together, and all the variables

(+.750n)*8n-2*8n+16*8n+1=0

We multiply parentheses

8n^2-2*8n+16*8n+1=0

Wy multiply elements

8n^2-16n+128n+1=0

We add all the numbers together, and all the variables

8n^2+112n+1=0

a = 8; b = 112; c = +1;
Δ = b2-4ac
Δ = 1122-4·8·1
Δ = 12512
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12512}=\sqrt{16*782}=\sqrt{16}*\sqrt{782}=4\sqrt{782}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{782}}{2*8}=\frac{-112-4\sqrt{782}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{782}}{2*8}=\frac{-112+4\sqrt{782}}{16}
$