7/2p-5/2p=20/3p+10

Solution for 7/2p-5/2p=20/3p+10 equation:

7/2p-5/2p=20/3p+10

We move all terms to the left:

7/2p-5/2p-(20/3p+10)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 3p+10)!=0

p∈R


We get rid of parentheses

7/2p-5/2p-20/3p-10=0

We calculate fractions


(-15p+7)/6p^2+(-40p)/6p^2-10=0

We multiply all the terms by the denominator


(-15p+7)+(-40p)-10*6p^2=0

Wy multiply elements

-60p^2+(-15p+7)+(-40p)=0

We get rid of parentheses

-60p^2-15p-40p+7=0

We add all the numbers together, and all the variables

-60p^2-55p+7=0

a = -60; b = -55; c = +7;
Δ = b2-4ac
Δ = -552-4·(-60)·7
Δ = 4705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{4705}}{2*-60}=\frac{55-\sqrt{4705}}{-120}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{4705}}{2*-60}=\frac{55+\sqrt{4705}}{-120}
$