1000-1/4p=-200+1/2p

Solution for 1000-1/4p=-200+1/2p equation:

1000-1/4p=-200+1/2p

We move all terms to the left:

1000-1/4p-(-200+1/2p)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 2p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-1/4p-(1/2p-200)+1000=0

We get rid of parentheses

-1/4p-1/2p+200+1000=0

We calculate fractions


(-2p)/8p^2+(-4p)/8p^2+200+1000=0

We add all the numbers together, and all the variables

(-2p)/8p^2+(-4p)/8p^2+1200=0

We multiply all the terms by the denominator


(-2p)+(-4p)+1200*8p^2=0

Wy multiply elements

9600p^2+(-2p)+(-4p)=0

We get rid of parentheses

9600p^2-2p-4p=0

We add all the numbers together, and all the variables

9600p^2-6p=0

a = 9600; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·9600·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*9600}=\frac{0}{19200}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*9600}=\frac{12}{19200}
=1/1600
$