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

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

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

We multiply parentheses ..

(+8p^2+40p-7p-35)=0

We get rid of parentheses

8p^2+40p-7p-35=0

We add all the numbers together, and all the variables

8p^2+33p-35=0

a = 8; b = 33; c = -35;
Δ = b2-4ac
Δ = 332-4·8·(-35)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-47}{2*8}=\frac{-80}{16}
=-5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+47}{2*8}=\frac{14}{16}
=7/8
$