5n^2-31n+30=0

Solution for 5n^2-31n+30=0 equation:

5n^2-31n+30=0

a = 5; b = -31; c = +30;
Δ = b2-4ac
Δ = -312-4·5·30
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-19}{2*5}=\frac{12}{10}
=1+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+19}{2*5}=\frac{50}{10}
=5
$