9n^2+16n-32=-4

Solution for 9n^2+16n-32=-4 equation:

9n^2+16n-32=-4

We move all terms to the left:

9n^2+16n-32-(-4)=0

We add all the numbers together, and all the variables

9n^2+16n-28=0

a = 9; b = 16; c = -28;
Δ = b2-4ac
Δ = 162-4·9·(-28)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{79}}{2*9}=\frac{-16-4\sqrt{79}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{79}}{2*9}=\frac{-16+4\sqrt{79}}{18}
$