6n^2-10n-19=0

Solution for 6n^2-10n-19=0 equation:

6n^2-10n-19=0

a = 6; b = -10; c = -19;
Δ = b2-4ac
Δ = -102-4·6·(-19)
Δ = 556
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{139}}{2*6}=\frac{10-2\sqrt{139}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{139}}{2*6}=\frac{10+2\sqrt{139}}{12}
$