20x^2-51x-9=0

Solution for 20x^2-51x-9=0 equation:

20x^2-51x-9=0

a = 20; b = -51; c = -9;
Δ = b2-4ac
Δ = -512-4·20·(-9)
Δ = 3321
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:

$\sqrt{\Delta}=\sqrt{3321}=\sqrt{81*41}=\sqrt{81}*\sqrt{41}=9\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-9\sqrt{41}}{2*20}=\frac{51-9\sqrt{41}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+9\sqrt{41}}{2*20}=\frac{51+9\sqrt{41}}{40}
$