1/2p+p=81

Solution for 1/2p+p=81 equation:

1/2p+p=81

We move all terms to the left:

1/2p+p-(81)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

p+1/2p-81=0

We multiply all the terms by the denominator


p*2p-81*2p+1=0

Wy multiply elements

2p^2-162p+1=0

a = 2; b = -162; c = +1;
Δ = b2-4ac
Δ = -1622-4·2·1
Δ = 26236
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:

$\sqrt{\Delta}=\sqrt{26236}=\sqrt{4*6559}=\sqrt{4}*\sqrt{6559}=2\sqrt{6559}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-2\sqrt{6559}}{2*2}=\frac{162-2\sqrt{6559}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+2\sqrt{6559}}{2*2}=\frac{162+2\sqrt{6559}}{4}
$