3/5p+1/4p=1/2

Solution for 3/5p+1/4p=1/2 equation:

3/5p+1/4p=1/2

We move all terms to the left:

3/5p+1/4p-(1/2)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We add all the numbers together, and all the variables

3/5p+1/4p-(+1/2)=0

We get rid of parentheses

3/5p+1/4p-1/2=0

We calculate fractions


(-80p^2)/80p^2+48p/80p^2+20p/80p^2=0

We multiply all the terms by the denominator


(-80p^2)+48p+20p=0

We add all the numbers together, and all the variables

(-80p^2)+68p=0

We get rid of parentheses

-80p^2+68p=0

a = -80; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-80)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-80}=\frac{-136}{-160}
=17/20
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-80}=\frac{0}{-160}
=0
$