3n^2=9n+4.75

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

3n^2=9n+4.75

We move all terms to the left:

3n^2-(9n+4.75)=0

We get rid of parentheses

3n^2-9n-4.75=0

a = 3; b = -9; c = -4.75;
Δ = b2-4ac
Δ = -92-4·3·(-4.75)
Δ = 138
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{138}}{2*3}=\frac{9-\sqrt{138}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{138}}{2*3}=\frac{9+\sqrt{138}}{6}
$