-5p(p-4)-3(-2-p)=p-2

Solution for -5p(p-4)-3(-2-p)=p-2 equation:

-5p(p-4)-3(-2-p)=p-2

We move all terms to the left:

-5p(p-4)-3(-2-p)-(p-2)=0

We add all the numbers together, and all the variables

-5p(p-4)-3(-1p-2)-(p-2)=0

We multiply parentheses

-5p^2+20p+3p-(p-2)+6=0

We get rid of parentheses

-5p^2+20p+3p-p+2+6=0

We add all the numbers together, and all the variables

-5p^2+22p+8=0

a = -5; b = 22; c = +8;
Δ = b2-4ac
Δ = 222-4·(-5)·8
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{161}}{2*-5}=\frac{-22-2\sqrt{161}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{161}}{2*-5}=\frac{-22+2\sqrt{161}}{-10}
$