16n2+1=101

Solution for 16n2+1=101 equation:

16n^2+1=101

We move all terms to the left:

16n^2+1-(101)=0

We add all the numbers together, and all the variables

16n^2-100=0

a = 16; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·16·(-100)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*16}=\frac{-80}{32}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*16}=\frac{80}{32}
=2+1/2
$