(5p-12)(6p+8)=0

Solution for (5p-12)(6p+8)=0 equation:

(5p-12)(6p+8)=0

We multiply parentheses ..

(+30p^2+40p-72p-96)=0

We get rid of parentheses

30p^2+40p-72p-96=0

We add all the numbers together, and all the variables

30p^2-32p-96=0

a = 30; b = -32; c = -96;
Δ = b2-4ac
Δ = -322-4·30·(-96)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-112}{2*30}=\frac{-80}{60}
=-1+1/3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+112}{2*30}=\frac{144}{60}
=2+2/5
$