13p^2-3p-9=0

Solution for 13p^2-3p-9=0 equation:

13p^2-3p-9=0

a = 13; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·13·(-9)
Δ = 477
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:

$\sqrt{\Delta}=\sqrt{477}=\sqrt{9*53}=\sqrt{9}*\sqrt{53}=3\sqrt{53}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{53}}{2*13}=\frac{3-3\sqrt{53}}{26}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{53}}{2*13}=\frac{3+3\sqrt{53}}{26}
$