10n^2-2n-3=0

Solution for 10n^2-2n-3=0 equation:

10n^2-2n-3=0

a = 10; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·10·(-3)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*10}=\frac{2-2\sqrt{31}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*10}=\frac{2+2\sqrt{31}}{20}
$