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

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

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

We move all terms to the left:

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


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 5p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


125p/250p^2+(-2p)/250p^2+(-6p)/250p^2-3=0

We multiply all the terms by the denominator


125p+(-2p)+(-6p)-3*250p^2=0

Wy multiply elements

-750p^2+125p+(-2p)+(-6p)=0

We get rid of parentheses

-750p^2+125p-2p-6p=0

We add all the numbers together, and all the variables

-750p^2+117p=0

a = -750; b = 117; c = 0;
Δ = b2-4ac
Δ = 1172-4·(-750)·0
Δ = 13689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13689}=117$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(117)-117}{2*-750}=\frac{-234}{-1500}
=39/250
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(117)+117}{2*-750}=\frac{0}{-1500}
=0
$