7n^2+2n-17=0

Solution for 7n^2+2n-17=0 equation:

7n^2+2n-17=0

a = 7; b = 2; c = -17;
Δ = b2-4ac
Δ = 22-4·7·(-17)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{30}}{2*7}=\frac{-2-4\sqrt{30}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{30}}{2*7}=\frac{-2+4\sqrt{30}}{14}
$