(5n)^2-5n-2=208

Solution for (5n)^2-5n-2=208 equation:

(5n)^2-5n-2=208

We move all terms to the left:

(5n)^2-5n-2-(208)=0

We add all the numbers together, and all the variables

5n^2-5n-210=0

a = 5; b = -5; c = -210;
Δ = b2-4ac
Δ = -52-4·5·(-210)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-65}{2*5}=\frac{-60}{10}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+65}{2*5}=\frac{70}{10}
=7
$