2n^2-10n-3=0

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

2n^2-10n-3=0

a = 2; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·2·(-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{-(-10)-2\sqrt{31}}{2*2}=\frac{10-2\sqrt{31}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{31}}{2*2}=\frac{10+2\sqrt{31}}{4}
$