6p^2-9p=24

Solution for 6p^2-9p=24 equation:

6p^2-9p=24

We move all terms to the left:

6p^2-9p-(24)=0

a = 6; b = -9; c = -24;
Δ = b2-4ac
Δ = -92-4·6·(-24)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{73}}{2*6}=\frac{9-3\sqrt{73}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{73}}{2*6}=\frac{9+3\sqrt{73}}{12}
$