10n2+4n=2

Solution for 10n2+4n=2 equation:

10n^2+4n=2

We move all terms to the left:

10n^2+4n-(2)=0

a = 10; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·10·(-2)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*10}=\frac{-4-4\sqrt{6}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*10}=\frac{-4+4\sqrt{6}}{20}
$