5/3p+3/2p=19/10

Solution for 5/3p+3/2p=19/10 equation:

5/3p+3/2p=19/10

We move all terms to the left:

5/3p+3/2p-(19/10)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

5/3p+3/2p-(+19/10)=0

We get rid of parentheses

5/3p+3/2p-19/10=0

We calculate fractions


(-228p^2)/60p^2+100p/60p^2+90p/60p^2=0

We multiply all the terms by the denominator


(-228p^2)+100p+90p=0

We add all the numbers together, and all the variables

(-228p^2)+190p=0

We get rid of parentheses

-228p^2+190p=0

a = -228; b = 190; c = 0;
Δ = b2-4ac
Δ = 1902-4·(-228)·0
Δ = 36100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36100}=190$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-190}{2*-228}=\frac{-380}{-456}
=5/6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+190}{2*-228}=\frac{0}{-456}
=0
$