2/5p+4=3/10p+5

Solution for 2/5p+4=3/10p+5 equation:

2/5p+4=3/10p+5

We move all terms to the left:

2/5p+4-(3/10p+5)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 10p+5)!=0

p∈R


We get rid of parentheses

2/5p-3/10p-5+4=0

We calculate fractions


20p/50p^2+(-15p)/50p^2-5+4=0

We add all the numbers together, and all the variables

20p/50p^2+(-15p)/50p^2-1=0

We multiply all the terms by the denominator


20p+(-15p)-1*50p^2=0

Wy multiply elements

-50p^2+20p+(-15p)=0

We get rid of parentheses

-50p^2+20p-15p=0

We add all the numbers together, and all the variables

-50p^2+5p=0

a = -50; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-50)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-50}=\frac{-10}{-100}
=1/10
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-50}=\frac{0}{-100}
=0
$