(2p+1)(p+7)=0

Solution for (2p+1)(p+7)=0 equation:

(2p+1)(p+7)=0

We multiply parentheses ..

(+2p^2+14p+p+7)=0

We get rid of parentheses

2p^2+14p+p+7=0

We add all the numbers together, and all the variables

2p^2+15p+7=0

a = 2; b = 15; c = +7;
Δ = b2-4ac
Δ = 152-4·2·7
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-13}{2*2}=\frac{-28}{4}
=-7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+13}{2*2}=\frac{-2}{4}
=-1/2
$