(8p+3)(5p+6)=0

Solution for (8p+3)(5p+6)=0 equation:

(8p+3)(5p+6)=0

We multiply parentheses ..

(+40p^2+48p+15p+18)=0

We get rid of parentheses

40p^2+48p+15p+18=0

We add all the numbers together, and all the variables

40p^2+63p+18=0

a = 40; b = 63; c = +18;
Δ = b2-4ac
Δ = 632-4·40·18
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-33}{2*40}=\frac{-96}{80}
=-1+1/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+33}{2*40}=\frac{-30}{80}
=-3/8
$