9(4n2+1)=1773

Solution for 9(4n2+1)=1773 equation:

9(4n^2+1)=1773

We move all terms to the left:

9(4n^2+1)-(1773)=0

We multiply parentheses

36n^2+9-1773=0

We add all the numbers together, and all the variables

36n^2-1764=0

a = 36; b = 0; c = -1764;
Δ = b2-4ac
Δ = 02-4·36·(-1764)
Δ = 254016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{254016}=504$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-504}{2*36}=\frac{-504}{72}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+504}{2*36}=\frac{504}{72}
=7
$