20x^2-111x-9=0

Solution for 20x^2-111x-9=0 equation:

20x^2-111x-9=0

a = 20; b = -111; c = -9;
Δ = b2-4ac
Δ = -1112-4·20·(-9)
Δ = 13041
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:

$\sqrt{\Delta}=\sqrt{13041}=\sqrt{81*161}=\sqrt{81}*\sqrt{161}=9\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-9\sqrt{161}}{2*20}=\frac{111-9\sqrt{161}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+9\sqrt{161}}{2*20}=\frac{111+9\sqrt{161}}{40}
$