64=4p(16/p)

Solution for 64=4p(16/p) equation:

64=4p(16/p)

We move all terms to the left:

64-(4p(16/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

-(4p(+16/p))+64=0

We multiply all the terms by the denominator


-(4p(+16+64*p))=0


We calculate terms in parentheses: -(4p(+16+64*p)), so:

4p(+16+64*p)

We add all the numbers together, and all the variables

4p(64p+16)

We multiply parentheses

256p^2+64p

Back to the equation:

-(256p^2+64p)


We get rid of parentheses

-256p^2-64p=0

a = -256; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·(-256)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*-256}=\frac{0}{-512}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*-256}=\frac{128}{-512}
=-1/4
$