6p^2-20p-9=0

Solution for 6p^2-20p-9=0 equation:

6p^2-20p-9=0

a = 6; b = -20; c = -9;
Δ = b2-4ac
Δ = -202-4·6·(-9)
Δ = 616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{154}}{2*6}=\frac{20-2\sqrt{154}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{154}}{2*6}=\frac{20+2\sqrt{154}}{12}
$