3n^2-15n+9=0

Solution for 3n^2-15n+9=0 equation:

3n^2-15n+9=0

a = 3; b = -15; c = +9;
Δ = b2-4ac
Δ = -152-4·3·9
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{13}}{2*3}=\frac{15-3\sqrt{13}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{13}}{2*3}=\frac{15+3\sqrt{13}}{6}
$