5(2+p)(p-8)=3

Solution for 5(2+p)(p-8)=3 equation:

5(2+p)(p-8)=3

We move all terms to the left:

5(2+p)(p-8)-(3)=0

We add all the numbers together, and all the variables

5(p+2)(p-8)-3=0

We multiply parentheses ..

5(+p^2-8p+2p-16)-3=0

We multiply parentheses

5p^2-40p+10p-80-3=0

We add all the numbers together, and all the variables

5p^2-30p-83=0

a = 5; b = -30; c = -83;
Δ = b2-4ac
Δ = -302-4·5·(-83)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-16\sqrt{10}}{2*5}=\frac{30-16\sqrt{10}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+16\sqrt{10}}{2*5}=\frac{30+16\sqrt{10}}{10}
$