3p^2-8p-45=0

Solution for 3p^2-8p-45=0 equation:

3p^2-8p-45=0

a = 3; b = -8; c = -45;
Δ = b2-4ac
Δ = -82-4·3·(-45)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{151}}{2*3}=\frac{8-2\sqrt{151}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{151}}{2*3}=\frac{8+2\sqrt{151}}{6}
$