1/3p+30=1/4p+60

Solution for 1/3p+30=1/4p+60 equation:

1/3p+30=1/4p+60

We move all terms to the left:

1/3p+30-(1/4p+60)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 4p+60)!=0

p∈R


We get rid of parentheses

1/3p-1/4p-60+30=0

We calculate fractions


4p/12p^2+(-3p)/12p^2-60+30=0

We add all the numbers together, and all the variables

4p/12p^2+(-3p)/12p^2-30=0

We multiply all the terms by the denominator


4p+(-3p)-30*12p^2=0

Wy multiply elements

-360p^2+4p+(-3p)=0

We get rid of parentheses

-360p^2+4p-3p=0

We add all the numbers together, and all the variables

-360p^2+p=0

a = -360; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-360)·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*-360}=\frac{-2}{-720}
=1/360
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-360}=\frac{0}{-720}
=0
$