-5p(p-8)-8p=-5-4p

Solution for -5p(p-8)-8p=-5-4p equation:

-5p(p-8)-8p=-5-4p

We move all terms to the left:

-5p(p-8)-8p-(-5-4p)=0

We add all the numbers together, and all the variables

-5p(p-8)-8p-(-4p-5)=0

We add all the numbers together, and all the variables

-8p-5p(p-8)-(-4p-5)=0

We multiply parentheses

-5p^2-8p+40p-(-4p-5)=0

We get rid of parentheses

-5p^2-8p+40p+4p+5=0

We add all the numbers together, and all the variables

-5p^2+36p+5=0

a = -5; b = 36; c = +5;
Δ = b2-4ac
Δ = 362-4·(-5)·5
Δ = 1396
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:

$\sqrt{\Delta}=\sqrt{1396}=\sqrt{4*349}=\sqrt{4}*\sqrt{349}=2\sqrt{349}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{349}}{2*-5}=\frac{-36-2\sqrt{349}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{349}}{2*-5}=\frac{-36+2\sqrt{349}}{-10}
$