3/2p+12/5p=13/20

Solution for 3/2p+12/5p=13/20 equation:

3/2p+12/5p=13/20

We move all terms to the left:

3/2p+12/5p-(13/20)=0


Domain of the equation: 2p!=0

p!=0/2

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

3/2p+12/5p-(+13/20)=0

We get rid of parentheses

3/2p+12/5p-13/20=0

We calculate fractions


(-650p^2)/400p^2+600p/400p^2+960p/400p^2=0

We multiply all the terms by the denominator


(-650p^2)+600p+960p=0

We add all the numbers together, and all the variables

(-650p^2)+1560p=0

We get rid of parentheses

-650p^2+1560p=0

a = -650; b = 1560; c = 0;
Δ = b2-4ac
Δ = 15602-4·(-650)·0
Δ = 2433600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2433600}=1560$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1560)-1560}{2*-650}=\frac{-3120}{-1300}
=2+2/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1560)+1560}{2*-650}=\frac{0}{-1300}
=0
$