6=6p-1/2p

Solution for 6=6p-1/2p equation:

6=6p-1/2p

We move all terms to the left:

6-(6p-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

-(+6p-1/2p)+6=0

We get rid of parentheses

-6p+1/2p+6=0

We multiply all the terms by the denominator


-6p*2p+6*2p+1=0

Wy multiply elements

-12p^2+12p+1=0

a = -12; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-12)·1
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{3}}{2*-12}=\frac{-12-8\sqrt{3}}{-24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{3}}{2*-12}=\frac{-12+8\sqrt{3}}{-24}
$