9n^2-39n+32=-4

Solution for 9n^2-39n+32=-4 equation:

9n^2-39n+32=-4

We move all terms to the left:

9n^2-39n+32-(-4)=0

We add all the numbers together, and all the variables

9n^2-39n+36=0

a = 9; b = -39; c = +36;
Δ = b2-4ac
Δ = -392-4·9·36
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-15}{2*9}=\frac{24}{18}
=1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+15}{2*9}=\frac{54}{18}
=3
$