5n^2-2n-2=0

Solution for 5n^2-2n-2=0 equation:

5n^2-2n-2=0

a = 5; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·5·(-2)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11}}{2*5}=\frac{2-2\sqrt{11}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11}}{2*5}=\frac{2+2\sqrt{11}}{10}
$