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

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

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

We move all terms to the left:

8/3p+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

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

We multiply parentheses

8/3p+6p-24+10=0

We multiply all the terms by the denominator


6p*3p-24*3p+10*3p+8=0

Wy multiply elements

18p^2-72p+30p+8=0

We add all the numbers together, and all the variables

18p^2-42p+8=0

a = 18; b = -42; c = +8;
Δ = b2-4ac
Δ = -422-4·18·8
Δ = 1188
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:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{33}}{2*18}=\frac{42-6\sqrt{33}}{36}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{33}}{2*18}=\frac{42+6\sqrt{33}}{36}
$