3-9n^2=-825

Solution for 3-9n^2=-825 equation:

3-9n^2=-825

We move all terms to the left:

3-9n^2-(-825)=0

We add all the numbers together, and all the variables

-9n^2+828=0

a = -9; b = 0; c = +828;
Δ = b2-4ac
Δ = 02-4·(-9)·828
Δ = 29808
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{29808}=\sqrt{1296*23}=\sqrt{1296}*\sqrt{23}=36\sqrt{23}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{23}}{2*-9}=\frac{0-36\sqrt{23}}{-18}
=-\frac{36\sqrt{23}}{-18}
=-\frac{2\sqrt{23}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{23}}{2*-9}=\frac{0+36\sqrt{23}}{-18}
=\frac{36\sqrt{23}}{-18}
=\frac{2\sqrt{23}}{-1}
$