1/2p-p=4

Solution for 1/2p-p=4 equation:

1/2p-p=4

We move all terms to the left:

1/2p-p-(4)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

-1p+1/2p-4=0

We multiply all the terms by the denominator


-1p*2p-4*2p+1=0

Wy multiply elements

-2p^2-8p+1=0

a = -2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-2)·1
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{2}}{2*-2}=\frac{8-6\sqrt{2}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*-2}=\frac{8+6\sqrt{2}}{-4}
$