4n^(2)+1=325

Solution for 4n^(2)+1=325 equation:

4n^(2)+1=325

We move all terms to the left:

4n^(2)+1-(325)=0

We add all the numbers together, and all the variables

4n^2-324=0

a = 4; b = 0; c = -324;
Δ = b2-4ac
Δ = 02-4·4·(-324)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*4}=\frac{-72}{8}
=-9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*4}=\frac{72}{8}
=9
$