1/6p+4=1/5p

Solution for 1/6p+4=1/5p equation:

1/6p+4=1/5p

We move all terms to the left:

1/6p+4-(1/5p)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 5p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1/6p-(+1/5p)+4=0

We get rid of parentheses

1/6p-1/5p+4=0

We calculate fractions


5p/30p^2+(-6p)/30p^2+4=0

We multiply all the terms by the denominator


5p+(-6p)+4*30p^2=0

Wy multiply elements

120p^2+5p+(-6p)=0

We get rid of parentheses

120p^2+5p-6p=0

We add all the numbers together, and all the variables

120p^2-1p=0

a = 120; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·120·0
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*120}=\frac{0}{240}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*120}=\frac{2}{240}
=1/120
$