(1/3)(9p+36)=48

Solution for (1/3)(9p+36)=48 equation:

(1/3)(9p+36)=48

We move all terms to the left:

(1/3)(9p+36)-(48)=0


Domain of the equation: 3)(9p+36)!=0

p∈R


We add all the numbers together, and all the variables

(+1/3)(9p+36)-48=0

We multiply parentheses ..

(+9p^2+1/3*36)-48=0

We multiply all the terms by the denominator


(+9p^2+1-48*3*36)=0

We get rid of parentheses

9p^2+1-48*3*36=0

We add all the numbers together, and all the variables

9p^2-5183=0

a = 9; b = 0; c = -5183;
Δ = b2-4ac
Δ = 02-4·9·(-5183)
Δ = 186588
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:

$\sqrt{\Delta}=\sqrt{186588}=\sqrt{36*5183}=\sqrt{36}*\sqrt{5183}=6\sqrt{5183}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5183}}{2*9}=\frac{0-6\sqrt{5183}}{18}
=-\frac{6\sqrt{5183}}{18}
=-\frac{\sqrt{5183}}{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5183}}{2*9}=\frac{0+6\sqrt{5183}}{18}
=\frac{6\sqrt{5183}}{18}
=\frac{\sqrt{5183}}{3}
$