1/4p=16-1/3p

Solution for 1/4p=16-1/3p equation:

1/4p=16-1/3p

We move all terms to the left:

1/4p-(16-1/3p)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1/4p-(-1/3p+16)=0

We get rid of parentheses

1/4p+1/3p-16=0

We calculate fractions


3p/12p^2+4p/12p^2-16=0

We multiply all the terms by the denominator


3p+4p-16*12p^2=0

We add all the numbers together, and all the variables

7p-16*12p^2=0

Wy multiply elements

-192p^2+7p=0

a = -192; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-192)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-192}=\frac{-14}{-384}
=7/192
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-192}=\frac{0}{-384}
=0
$