9x^2-16x-1=0

Solution for 9x^2-16x-1=0 equation:

9x^2-16x-1=0

a = 9; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·9·(-1)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{73}}{2*9}=\frac{16-2\sqrt{73}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{73}}{2*9}=\frac{16+2\sqrt{73}}{18}
$