3(p+8)=-6(p+6)/3

Solution for 3(p+8)=-6(p+6)/3 equation:

3(p+8)=-6(p+6)/3

We move all terms to the left:

3(p+8)-(-6(p+6)/3)=0

We multiply parentheses

3p-(-6(p+6)/3)+24=0

We multiply all the terms by the denominator


3p*3)-(-6(p+6)+24*3)=0

We add all the numbers together, and all the variables

3p*3)-(-6(p+6)=0

We multiply parentheses

3p*3)-(-6p-36=0

Wy multiply elements

9p^2-6p-36=0

a = 9; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·9·(-36)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{37}}{2*9}=\frac{6-6\sqrt{37}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{37}}{2*9}=\frac{6+6\sqrt{37}}{18}
$