7n^2-47n-14=0

Solution for 7n^2-47n-14=0 equation:

7n^2-47n-14=0

a = 7; b = -47; c = -14;
Δ = b2-4ac
Δ = -472-4·7·(-14)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-51}{2*7}=\frac{-4}{14}
=-2/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+51}{2*7}=\frac{98}{14}
=7
$