2+2/3p+3(2/3p-8)=10

Solution for 2+2/3p+3(2/3p-8)=10 equation:

2+2/3p+3(2/3p-8)=10

We move all terms to the left:

2+2/3p+3(2/3p-8)-(10)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 3p-8)!=0

p∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

2/3p+6p-24-8=0

We multiply all the terms by the denominator


6p*3p-24*3p-8*3p+2=0

Wy multiply elements

18p^2-72p-24p+2=0

We add all the numbers together, and all the variables

18p^2-96p+2=0

a = 18; b = -96; c = +2;
Δ = b2-4ac
Δ = -962-4·18·2
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-36\sqrt{7}}{2*18}=\frac{96-36\sqrt{7}}{36}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+36\sqrt{7}}{2*18}=\frac{96+36\sqrt{7}}{36}
$