22/3p+3(2/3p-8)=10

Solution for 22/3p+3(2/3p-8)=10 equation:

22/3p+3(2/3p-8)=10

We move all terms to the left:

22/3p+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 multiply parentheses

22/3p+6p-24-10=0

We multiply all the terms by the denominator


6p*3p-24*3p-10*3p+22=0

Wy multiply elements

18p^2-72p-30p+22=0

We add all the numbers together, and all the variables

18p^2-102p+22=0

a = 18; b = -102; c = +22;
Δ = b2-4ac
Δ = -1022-4·18·22
Δ = 8820
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:

$\sqrt{\Delta}=\sqrt{8820}=\sqrt{1764*5}=\sqrt{1764}*\sqrt{5}=42\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-42\sqrt{5}}{2*18}=\frac{102-42\sqrt{5}}{36}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+42\sqrt{5}}{2*18}=\frac{102+42\sqrt{5}}{36}
$