2/3p+2+1/5p-4=7/5

Solution for 2/3p+2+1/5p-4=7/5 equation:

2/3p+2+1/5p-4=7/5

We move all terms to the left:

2/3p+2+1/5p-4-(7/5)=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

2/3p+1/5p+2-4-(+7/5)=0

We add all the numbers together, and all the variables

2/3p+1/5p-2-(+7/5)=0

We get rid of parentheses

2/3p+1/5p-2-7/5=0

We calculate fractions


250p/375p^2+3p/375p^2+(-21p)/375p^2-2=0

We multiply all the terms by the denominator


250p+3p+(-21p)-2*375p^2=0

We add all the numbers together, and all the variables

253p+(-21p)-2*375p^2=0

Wy multiply elements

-750p^2+253p+(-21p)=0

We get rid of parentheses

-750p^2+253p-21p=0

We add all the numbers together, and all the variables

-750p^2+232p=0

a = -750; b = 232; c = 0;
Δ = b2-4ac
Δ = 2322-4·(-750)·0
Δ = 53824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{53824}=232$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(232)-232}{2*-750}=\frac{-464}{-1500}
=116/375
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(232)+232}{2*-750}=\frac{0}{-1500}
=0
$