2x2-17x-1=0

Solution for 2x2-17x-1=0 equation:

2x^2-17x-1=0

a = 2; b = -17; c = -1;
Δ = b2-4ac
Δ = -172-4·2·(-1)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{33}}{2*2}=\frac{17-3\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{33}}{2*2}=\frac{17+3\sqrt{33}}{4}
$