1/2p-12=3/12p-18

Solution for 1/2p-12=3/12p-18 equation:

1/2p-12=3/12p-18

We move all terms to the left:

1/2p-12-(3/12p-18)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 12p-18)!=0

p∈R


We get rid of parentheses

1/2p-3/12p+18-12=0

We calculate fractions


12p/24p^2+(-6p)/24p^2+18-12=0

We add all the numbers together, and all the variables

12p/24p^2+(-6p)/24p^2+6=0

We multiply all the terms by the denominator


12p+(-6p)+6*24p^2=0

Wy multiply elements

144p^2+12p+(-6p)=0

We get rid of parentheses

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