20x^2-18x-9=0

Solution for 20x^2-18x-9=0 equation:

20x^2-18x-9=0

a = 20; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·20·(-9)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{29}}{2*20}=\frac{18-6\sqrt{29}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{29}}{2*20}=\frac{18+6\sqrt{29}}{40}
$