3p(3-p)=3(3p-16)

Solution for 3p(3-p)=3(3p-16) equation:

3p(3-p)=3(3p-16)

We move all terms to the left:

3p(3-p)-(3(3p-16))=0

We add all the numbers together, and all the variables

3p(-1p+3)-(3(3p-16))=0

We multiply parentheses

-3p^2+9p-(3(3p-16))=0


We calculate terms in parentheses: -(3(3p-16)), so:

3(3p-16)

We multiply parentheses

9p-48

Back to the equation:

-(9p-48)


We get rid of parentheses

-3p^2+9p-9p+48=0

We add all the numbers together, and all the variables

-3p^2+48=0

a = -3; b = 0; c = +48;
Δ = b2-4ac
Δ = 02-4·(-3)·48
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-3}=\frac{-24}{-6}
=+4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-3}=\frac{24}{-6}
=-4
$