14-1/2p=1/4p-4

Solution for 14-1/2p=1/4p-4 equation:

14-1/2p=1/4p-4

We move all terms to the left:

14-1/2p-(1/4p-4)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 4p-4)!=0

p∈R


We get rid of parentheses

-1/2p-1/4p+4+14=0

We calculate fractions


(-4p)/8p^2+(-2p)/8p^2+4+14=0

We add all the numbers together, and all the variables

(-4p)/8p^2+(-2p)/8p^2+18=0

We multiply all the terms by the denominator


(-4p)+(-2p)+18*8p^2=0

Wy multiply elements

144p^2+(-4p)+(-2p)=0

We get rid of parentheses

144p^2-4p-2p=0

We add all the numbers together, and all the variables

144p^2-6p=0

a = 144; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·144·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*144}=\frac{0}{288}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*144}=\frac{12}{288}
=1/24
$