2/3p-2/7p+12=6

Solution for 2/3p-2/7p+12=6 equation:

2/3p-2/7p+12=6

We move all terms to the left:

2/3p-2/7p+12-(6)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 7p!=0

p!=0/7

p!=0

p∈R


We add all the numbers together, and all the variables

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

We calculate fractions


14p/21p^2+(-6p)/21p^2+6=0

We multiply all the terms by the denominator


14p+(-6p)+6*21p^2=0

Wy multiply elements

126p^2+14p+(-6p)=0

We get rid of parentheses

126p^2+14p-6p=0

We add all the numbers together, and all the variables

126p^2+8p=0

a = 126; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·126·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*126}=\frac{-16}{252}
=-4/63
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*126}=\frac{0}{252}
=0
$