9x^2-42x-17=0

Solution for 9x^2-42x-17=0 equation:

9x^2-42x-17=0

a = 9; b = -42; c = -17;
Δ = b2-4ac
Δ = -422-4·9·(-17)
Δ = 2376
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:

$\sqrt{\Delta}=\sqrt{2376}=\sqrt{36*66}=\sqrt{36}*\sqrt{66}=6\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{66}}{2*9}=\frac{42-6\sqrt{66}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{66}}{2*9}=\frac{42+6\sqrt{66}}{18}
$