3p-8=6(1/2p-8)

Solution for 3p-8=6(1/2p-8) equation:

3p-8=6(1/2p-8)

We move all terms to the left:

3p-8-(6(1/2p-8))=0


Domain of the equation: 2p-8))!=0

p∈R


We multiply all the terms by the denominator


3p*2p-8*2p-8))-(6(1-8))=0

We add all the numbers together, and all the variables

3p*2p-8*2p-8))-(6(-7))=0

We add all the numbers together, and all the variables

3p*2p-8*2p=0

Wy multiply elements

6p^2-16p=0

a = 6; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·6·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*6}=\frac{0}{12}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*6}=\frac{32}{12}
=2+2/3
$