-1/3p+1/5p=7/45

Solution for -1/3p+1/5p=7/45 equation:

-1/3p+1/5p=7/45

We move all terms to the left:

-1/3p+1/5p-(7/45)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

-1/3p+1/5p-(+7/45)=0

We get rid of parentheses

-1/3p+1/5p-7/45=0

We calculate fractions


(-525p^2)/2700p^2+(-900p)/2700p^2+540p/2700p^2=0

We multiply all the terms by the denominator


(-525p^2)+(-900p)+540p=0

We add all the numbers together, and all the variables

(-525p^2)+540p+(-900p)=0

We get rid of parentheses

-525p^2+540p-900p=0

We add all the numbers together, and all the variables

-525p^2-360p=0

a = -525; b = -360; c = 0;
Δ = b2-4ac
Δ = -3602-4·(-525)·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-360}{2*-525}=\frac{0}{-1050}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+360}{2*-525}=\frac{720}{-1050}
=-24/35
$