5p(p-8)-(3p-12)=6

Solution for 5p(p-8)-(3p-12)=6 equation:

5p(p-8)-(3p-12)=6

We move all terms to the left:

5p(p-8)-(3p-12)-(6)=0

We multiply parentheses

5p^2-40p-(3p-12)-6=0

We get rid of parentheses

5p^2-40p-3p+12-6=0

We add all the numbers together, and all the variables

5p^2-43p+6=0

a = 5; b = -43; c = +6;
Δ = b2-4ac
Δ = -432-4·5·6
Δ = 1729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-\sqrt{1729}}{2*5}=\frac{43-\sqrt{1729}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{1729}}{2*5}=\frac{43+\sqrt{1729}}{10}
$