5n^2-67n+216=0

Solution for 5n^2-67n+216=0 equation:

5n^2-67n+216=0

a = 5; b = -67; c = +216;
Δ = b2-4ac
Δ = -672-4·5·216
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{-(-67)-13}{2*5}=\frac{54}{10}
=5+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+13}{2*5}=\frac{80}{10}
=8
$