7n^2=14n+2

Solution for 7n^2=14n+2 equation:

7n^2=14n+2

We move all terms to the left:

7n^2-(14n+2)=0

We get rid of parentheses

7n^2-14n-2=0

a = 7; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·7·(-2)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{7}}{2*7}=\frac{14-6\sqrt{7}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{7}}{2*7}=\frac{14+6\sqrt{7}}{14}
$