10n^2-31n-14=0

Solution for 10n^2-31n-14=0 equation:

10n^2-31n-14=0

a = 10; b = -31; c = -14;
Δ = b2-4ac
Δ = -312-4·10·(-14)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-39}{2*10}=\frac{-8}{20}
=-2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+39}{2*10}=\frac{70}{20}
=3+1/2
$