p-4=28/p=32

Solution for p-4=28/p=32 equation:

p-4=28/p=32

We move all terms to the left:

p-4-(28/p)=0


Domain of the equation: p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

p-(+28/p)-4=0

We get rid of parentheses

p-28/p-4=0

We multiply all the terms by the denominator


p*p-4*p-28=0

We add all the numbers together, and all the variables

-4p+p*p-28=0

Wy multiply elements

p^2-4p-28=0

a = 1; b = -4; c = -28;
Δ = b2-4ac
Δ = -42-4·1·(-28)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{2}}{2*1}=\frac{4-8\sqrt{2}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{2}}{2*1}=\frac{4+8\sqrt{2}}{2}
$