(3n+5n)10n=5

Solution for (3n+5n)10n=5 equation:

(3n+5n)10n=5

We move all terms to the left:

(3n+5n)10n-(5)=0

We add all the numbers together, and all the variables

(+8n)10n-5=0

We multiply parentheses

80n^2-5=0

a = 80; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·80·(-5)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*80}=\frac{-40}{160}
=-1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*80}=\frac{40}{160}
=1/4
$