1/5p+7=1/4p

Solution for 1/5p+7=1/4p equation:

1/5p+7=1/4p

We move all terms to the left:

1/5p+7-(1/4p)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 4p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1/5p-(+1/4p)+7=0

We get rid of parentheses

1/5p-1/4p+7=0

We calculate fractions


4p/20p^2+(-5p)/20p^2+7=0

We multiply all the terms by the denominator


4p+(-5p)+7*20p^2=0

Wy multiply elements

140p^2+4p+(-5p)=0

We get rid of parentheses

140p^2+4p-5p=0

We add all the numbers together, and all the variables

140p^2-1p=0

a = 140; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·140·0
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*140}=\frac{0}{280}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*140}=\frac{2}{280}
=1/140
$