7n^2-33n-400=0

Solution for 7n^2-33n-400=0 equation:

7n^2-33n-400=0

a = 7; b = -33; c = -400;
Δ = b2-4ac
Δ = -332-4·7·(-400)
Δ = 12289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-\sqrt{12289}}{2*7}=\frac{33-\sqrt{12289}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{12289}}{2*7}=\frac{33+\sqrt{12289}}{14}
$