-8p(-3+5p)=-38-8

Solution for -8p(-3+5p)=-38-8 equation:

-8p(-3+5p)=-38-8

We move all terms to the left:

-8p(-3+5p)-(-38-8)=0

We add all the numbers together, and all the variables

-8p(5p-3)-(-46)=0

We add all the numbers together, and all the variables

-8p(5p-3)+46=0

We multiply parentheses

-40p^2+24p+46=0

a = -40; b = 24; c = +46;
Δ = b2-4ac
Δ = 242-4·(-40)·46
Δ = 7936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7936}=\sqrt{256*31}=\sqrt{256}*\sqrt{31}=16\sqrt{31}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{31}}{2*-40}=\frac{-24-16\sqrt{31}}{-80}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{31}}{2*-40}=\frac{-24+16\sqrt{31}}{-80}
$