1/4-7/10p=1/20p

Solution for 1/4-7/10p=1/20p equation:

1/4-7/10p=1/20p

We move all terms to the left:

1/4-7/10p-(1/20p)=0


Domain of the equation: 10p!=0

p!=0/10

p!=0

p∈R



Domain of the equation: 20p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-7/10p-(+1/20p)+1/4=0

We get rid of parentheses

-7/10p-1/20p+1/4=0

We calculate fractions


400p^2/3200p^2+(-2240p)/3200p^2+(-160p)/3200p^2=0

We multiply all the terms by the denominator


400p^2+(-2240p)+(-160p)=0

We get rid of parentheses

400p^2-2240p-160p=0

We add all the numbers together, and all the variables

400p^2-2400p=0

a = 400; b = -2400; c = 0;
Δ = b2-4ac
Δ = -24002-4·400·0
Δ = 5760000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5760000}=2400$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2400)-2400}{2*400}=\frac{0}{800}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2400)+2400}{2*400}=\frac{4800}{800}
=6
$