5n^2+8n+1=5

Solution for 5n^2+8n+1=5 equation:

5n^2+8n+1=5

We move all terms to the left:

5n^2+8n+1-(5)=0

We add all the numbers together, and all the variables

5n^2+8n-4=0

a = 5; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·5·(-4)
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*5}=\frac{-20}{10}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*5}=\frac{4}{10}
=2/5
$