(p+7)(6p-8)=0

Solution for (p+7)(6p-8)=0 equation:

(p+7)(6p-8)=0

We multiply parentheses ..

(+6p^2-8p+42p-56)=0

We get rid of parentheses

6p^2-8p+42p-56=0

We add all the numbers together, and all the variables

6p^2+34p-56=0

a = 6; b = 34; c = -56;
Δ = b2-4ac
Δ = 342-4·6·(-56)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-50}{2*6}=\frac{-84}{12}
=-7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+50}{2*6}=\frac{16}{12}
=1+1/3
$