2p-8=12-1/2p

Solution for 2p-8=12-1/2p equation:

2p-8=12-1/2p

We move all terms to the left:

2p-8-(12-1/2p)=0


Domain of the equation: 2p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

2p-(-1/2p+12)-8=0

We get rid of parentheses

2p+1/2p-12-8=0

We multiply all the terms by the denominator


2p*2p-12*2p-8*2p+1=0

Wy multiply elements

4p^2-24p-16p+1=0

We add all the numbers together, and all the variables

4p^2-40p+1=0

a = 4; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·4·1
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{11}}{2*4}=\frac{40-12\sqrt{11}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{11}}{2*4}=\frac{40+12\sqrt{11}}{8}
$