733=4n2+108

Solution for 733=4n2+108 equation:

733=4n^2+108

We move all terms to the left:

733-(4n^2+108)=0

We get rid of parentheses

-4n^2-108+733=0

We add all the numbers together, and all the variables

-4n^2+625=0

a = -4; b = 0; c = +625;
Δ = b2-4ac
Δ = 02-4·(-4)·625
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*-4}=\frac{-100}{-8}
=12+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*-4}=\frac{100}{-8}
=-12+1/2
$