8n+10=1/25n

Solution for 8n+10=1/25n equation:

8n+10=1/25n

We move all terms to the left:

8n+10-(1/25n)=0


Domain of the equation: 25n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

8n-(+1/25n)+10=0

We get rid of parentheses

8n-1/25n+10=0

We multiply all the terms by the denominator


8n*25n+10*25n-1=0

Wy multiply elements

200n^2+250n-1=0

a = 200; b = 250; c = -1;
Δ = b2-4ac
Δ = 2502-4·200·(-1)
Δ = 63300
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:

$\sqrt{\Delta}=\sqrt{63300}=\sqrt{100*633}=\sqrt{100}*\sqrt{633}=10\sqrt{633}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-10\sqrt{633}}{2*200}=\frac{-250-10\sqrt{633}}{400}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+10\sqrt{633}}{2*200}=\frac{-250+10\sqrt{633}}{400}
$