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

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

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

We move all terms to the left:

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


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 5p+1)!=0

p∈R


We get rid of parentheses

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

We calculate fractions


15p/40p^2+(-16p)/40p^2+5p/40p^2-1=0

We multiply all the terms by the denominator


15p+(-16p)+5p-1*40p^2=0

We add all the numbers together, and all the variables

20p+(-16p)-1*40p^2=0

Wy multiply elements

-40p^2+20p+(-16p)=0

We get rid of parentheses

-40p^2+20p-16p=0

We add all the numbers together, and all the variables

-40p^2+4p=0

a = -40; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-40)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-40}=\frac{-8}{-80}
=1/10
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-40}=\frac{0}{-80}
=0
$