7n^2+4n-14=0

Solution for 7n^2+4n-14=0 equation:

7n^2+4n-14=0

a = 7; b = 4; c = -14;
Δ = b2-4ac
Δ = 42-4·7·(-14)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{102}}{2*7}=\frac{-4-2\sqrt{102}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{102}}{2*7}=\frac{-4+2\sqrt{102}}{14}
$