10n^2-6n-14=0

Solution for 10n^2-6n-14=0 equation:

10n^2-6n-14=0

a = 10; b = -6; c = -14;
Δ = b2-4ac
Δ = -62-4·10·(-14)
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{149}}{2*10}=\frac{6-2\sqrt{149}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{149}}{2*10}=\frac{6+2\sqrt{149}}{20}
$