9n+3n^2+4.75=0

Solution for 9n+3n^2+4.75=0 equation:

9n+3n^2+4.75=0

a = 3; b = 9; c = +4.75;
Δ = b2-4ac
Δ = 92-4·3·4.75
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-2\sqrt{6}}{2*3}=\frac{-9-2\sqrt{6}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+2\sqrt{6}}{2*3}=\frac{-9+2\sqrt{6}}{6}
$