5=-6n^2+17n

Solution for 5=-6n^2+17n equation:

5=-6n^2+17n

We move all terms to the left:

5-(-6n^2+17n)=0

We get rid of parentheses

6n^2-17n+5=0

a = 6; b = -17; c = +5;
Δ = b2-4ac
Δ = -172-4·6·5
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*6}=\frac{4}{12}
=1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*6}=\frac{30}{12}
=2+1/2
$