(p-3)(7p+8)=0

Solution for (p-3)(7p+8)=0 equation:

(p-3)(7p+8)=0

We multiply parentheses ..

(+7p^2+8p-21p-24)=0

We get rid of parentheses

7p^2+8p-21p-24=0

We add all the numbers together, and all the variables

7p^2-13p-24=0

a = 7; b = -13; c = -24;
Δ = b2-4ac
Δ = -132-4·7·(-24)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*7}=\frac{-16}{14}
=-1+1/7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*7}=\frac{42}{14}
=3
$