17x^2-32x-2=0

Solution for 17x^2-32x-2=0 equation:

17x^2-32x-2=0

a = 17; b = -32; c = -2;
Δ = b2-4ac
Δ = -322-4·17·(-2)
Δ = 1160
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:

$\sqrt{\Delta}=\sqrt{1160}=\sqrt{4*290}=\sqrt{4}*\sqrt{290}=2\sqrt{290}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{290}}{2*17}=\frac{32-2\sqrt{290}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{290}}{2*17}=\frac{32+2\sqrt{290}}{34}
$