4-9n^2=-28

Solution for 4-9n^2=-28 equation:

4-9n^2=-28

We move all terms to the left:

4-9n^2-(-28)=0

We add all the numbers together, and all the variables

-9n^2+32=0

a = -9; b = 0; c = +32;
Δ = b2-4ac
Δ = 02-4·(-9)·32
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-9}=\frac{0-24\sqrt{2}}{-18}
=-\frac{24\sqrt{2}}{-18}
=-\frac{4\sqrt{2}}{-3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-9}=\frac{0+24\sqrt{2}}{-18}
=\frac{24\sqrt{2}}{-18}
=\frac{4\sqrt{2}}{-3}
$