(5p+2)(8p+7)=0

Solution for (5p+2)(8p+7)=0 equation:

(5p+2)(8p+7)=0

We multiply parentheses ..

(+40p^2+35p+16p+14)=0

We get rid of parentheses

40p^2+35p+16p+14=0

We add all the numbers together, and all the variables

40p^2+51p+14=0

a = 40; b = 51; c = +14;
Δ = b2-4ac
Δ = 512-4·40·14
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-19}{2*40}=\frac{-70}{80}
=-7/8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+19}{2*40}=\frac{-32}{80}
=-2/5
$