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

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

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

We move all terms to the left:

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


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 5p+11)!=0

p∈R


We get rid of parentheses

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

We calculate fractions


(-25p)/10p^2+(-2p)/10p^2-11+2=0

We add all the numbers together, and all the variables

(-25p)/10p^2+(-2p)/10p^2-9=0

We multiply all the terms by the denominator


(-25p)+(-2p)-9*10p^2=0

Wy multiply elements

-90p^2+(-25p)+(-2p)=0

We get rid of parentheses

-90p^2-25p-2p=0

We add all the numbers together, and all the variables

-90p^2-27p=0

a = -90; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-90)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-90}=\frac{0}{-180}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-90}=\frac{54}{-180}
=-3/10
$