1/6p+12=1/8p+20

Solution for 1/6p+12=1/8p+20 equation:

1/6p+12=1/8p+20

We move all terms to the left:

1/6p+12-(1/8p+20)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 8p+20)!=0

p∈R


We get rid of parentheses

1/6p-1/8p-20+12=0

We calculate fractions


8p/48p^2+(-6p)/48p^2-20+12=0

We add all the numbers together, and all the variables

8p/48p^2+(-6p)/48p^2-8=0

We multiply all the terms by the denominator


8p+(-6p)-8*48p^2=0

Wy multiply elements

-384p^2+8p+(-6p)=0

We get rid of parentheses

-384p^2+8p-6p=0

We add all the numbers together, and all the variables

-384p^2+2p=0

a = -384; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-384)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-384}=\frac{-4}{-768}
=1/192
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-384}=\frac{0}{-768}
=0
$