-17x^2-14x-1=0

Solution for -17x^2-14x-1=0 equation:

-17x^2-14x-1=0

a = -17; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·(-17)·(-1)
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8\sqrt{2}}{2*-17}=\frac{14-8\sqrt{2}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8\sqrt{2}}{2*-17}=\frac{14+8\sqrt{2}}{-34}
$