7n^2-17n-8=0

Solution for 7n^2-17n-8=0 equation:

7n^2-17n-8=0

a = 7; b = -17; c = -8;
Δ = b2-4ac
Δ = -172-4·7·(-8)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{57}}{2*7}=\frac{17-3\sqrt{57}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{57}}{2*7}=\frac{17+3\sqrt{57}}{14}
$