-2/5p+2=1/3p+11

Solution for -2/5p+2=1/3p+11 equation:

-2/5p+2=1/3p+11

We move all terms to the left:

-2/5p+2-(1/3p+11)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 3p+11)!=0

p∈R


We get rid of parentheses

-2/5p-1/3p-11+2=0

We calculate fractions


(-6p)/15p^2+(-5p)/15p^2-11+2=0

We add all the numbers together, and all the variables

(-6p)/15p^2+(-5p)/15p^2-9=0

We multiply all the terms by the denominator


(-6p)+(-5p)-9*15p^2=0

Wy multiply elements

-135p^2+(-6p)+(-5p)=0

We get rid of parentheses

-135p^2-6p-5p=0

We add all the numbers together, and all the variables

-135p^2-11p=0

a = -135; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-135)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-135}=\frac{0}{-270}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-135}=\frac{22}{-270}
=-11/135
$