1/6p-5=1/2p+2

Solution for 1/6p-5=1/2p+2 equation:

1/6p-5=1/2p+2

We move all terms to the left:

1/6p-5-(1/2p+2)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 2p+2)!=0

p∈R


We get rid of parentheses

1/6p-1/2p-2-5=0

We calculate fractions


2p/12p^2+(-6p)/12p^2-2-5=0

We add all the numbers together, and all the variables

2p/12p^2+(-6p)/12p^2-7=0

We multiply all the terms by the denominator


2p+(-6p)-7*12p^2=0

Wy multiply elements

-84p^2+2p+(-6p)=0

We get rid of parentheses

-84p^2+2p-6p=0

We add all the numbers together, and all the variables

-84p^2-4p=0

a = -84; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-84)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-84}=\frac{0}{-168}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-84}=\frac{8}{-168}
=-1/21
$