17x2-6x-9=0

Solution for 17x2-6x-9=0 equation:

17x^2-6x-9=0

a = 17; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·17·(-9)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18\sqrt{2}}{2*17}=\frac{6-18\sqrt{2}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18\sqrt{2}}{2*17}=\frac{6+18\sqrt{2}}{34}
$