4n^2=5+8n

Solution for 4n^2=5+8n equation:

4n^2=5+8n

We move all terms to the left:

4n^2-(5+8n)=0

We add all the numbers together, and all the variables

4n^2-(8n+5)=0

We get rid of parentheses

4n^2-8n-5=0

a = 4; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·4·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*4}=\frac{-4}{8}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*4}=\frac{20}{8}
=2+1/2
$