7n^2-22n-19=0

Solution for 7n^2-22n-19=0 equation:

7n^2-22n-19=0

a = 7; b = -22; c = -19;
Δ = b2-4ac
Δ = -222-4·7·(-19)
Δ = 1016
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:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{254}}{2*7}=\frac{22-2\sqrt{254}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{254}}{2*7}=\frac{22+2\sqrt{254}}{14}
$