-3n^2+29n-66=0

Solution for -3n^2+29n-66=0 equation:

-3n^2+29n-66=0

a = -3; b = 29; c = -66;
Δ = b2-4ac
Δ = 292-4·(-3)·(-66)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-7}{2*-3}=\frac{-36}{-6}
=+6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+7}{2*-3}=\frac{-22}{-6}
=3+2/3
$