7n^2-47n-72=0

Solution for 7n^2-47n-72=0 equation:

7n^2-47n-72=0

a = 7; b = -47; c = -72;
Δ = b2-4ac
Δ = -472-4·7·(-72)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-65}{2*7}=\frac{-18}{14}
=-1+2/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+65}{2*7}=\frac{112}{14}
=8
$