9x^2-20x-1=0

Solution for 9x^2-20x-1=0 equation:

9x^2-20x-1=0

a = 9; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·9·(-1)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{109}}{2*9}=\frac{20-2\sqrt{109}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{109}}{2*9}=\frac{20+2\sqrt{109}}{18}
$