(2/3)p-8=-2p+1+7

Solution for (2/3)p-8=-2p+1+7 equation:

(2/3)p-8=-2p+1+7

We move all terms to the left:

(2/3)p-8-(-2p+1+7)=0


Domain of the equation: 3)p!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

2p^2-(-2p+8)-8=0

We get rid of parentheses

2p^2+2p-8-8=0

We add all the numbers together, and all the variables

2p^2+2p-16=0

a = 2; b = 2; c = -16;
Δ = b2-4ac
Δ = 22-4·2·(-16)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{33}}{2*2}=\frac{-2-2\sqrt{33}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{33}}{2*2}=\frac{-2+2\sqrt{33}}{4}
$