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

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

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

We move all terms to the left:

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)+10=0

We multiply parentheses

2/3p+6p-24+10=0

We multiply all the terms by the denominator


6p*3p-24*3p+10*3p+2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

18p^2-42p+2=0

a = 18; b = -42; c = +2;
Δ = b2-4ac
Δ = -422-4·18·2
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-18\sqrt{5}}{2*18}=\frac{42-18\sqrt{5}}{36}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+18\sqrt{5}}{2*18}=\frac{42+18\sqrt{5}}{36}
$