7n^2-14n-49=0

Solution for 7n^2-14n-49=0 equation:

7n^2-14n-49=0

a = 7; b = -14; c = -49;
Δ = b2-4ac
Δ = -142-4·7·(-49)
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-28\sqrt{2}}{2*7}=\frac{14-28\sqrt{2}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+28\sqrt{2}}{2*7}=\frac{14+28\sqrt{2}}{14}
$