1/4p-6=2/7p+12

Solution for 1/4p-6=2/7p+12 equation:

1/4p-6=2/7p+12

We move all terms to the left:

1/4p-6-(2/7p+12)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 7p+12)!=0

p∈R


We get rid of parentheses

1/4p-2/7p-12-6=0

We calculate fractions


7p/28p^2+(-8p)/28p^2-12-6=0

We add all the numbers together, and all the variables

7p/28p^2+(-8p)/28p^2-18=0

We multiply all the terms by the denominator


7p+(-8p)-18*28p^2=0

Wy multiply elements

-504p^2+7p+(-8p)=0

We get rid of parentheses

-504p^2+7p-8p=0

We add all the numbers together, and all the variables

-504p^2-1p=0

a = -504; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-504)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-504}=\frac{0}{-1008}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-504}=\frac{2}{-1008}
=-1/504
$