2/6p+3=3/7p+1

Solution for 2/6p+3=3/7p+1 equation:

2/6p+3=3/7p+1

We move all terms to the left:

2/6p+3-(3/7p+1)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 7p+1)!=0

p∈R


We get rid of parentheses

2/6p-3/7p-1+3=0

We calculate fractions


14p/42p^2+(-18p)/42p^2-1+3=0

We add all the numbers together, and all the variables

14p/42p^2+(-18p)/42p^2+2=0

We multiply all the terms by the denominator


14p+(-18p)+2*42p^2=0

Wy multiply elements

84p^2+14p+(-18p)=0

We get rid of parentheses

84p^2+14p-18p=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
$