2n^2-n-406=0

Solution for 2n^2-n-406=0 equation:

2n^2-n-406=0

We add all the numbers together, and all the variables

2n^2-1n-406=0

a = 2; b = -1; c = -406;
Δ = b2-4ac
Δ = -12-4·2·(-406)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-57}{2*2}=\frac{-56}{4}
=-14
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+57}{2*2}=\frac{58}{4}
=14+1/2
$