8-1/4p=-1/2p

Solution for 8-1/4p=-1/2p equation:

8-1/4p=-1/2p

We move all terms to the left:

8-1/4p-(-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 get rid of parentheses

-1/4p+1/2p+8=0

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

64p^2+4p+(-2p)=0

We get rid of parentheses

64p^2+4p-2p=0

We add all the numbers together, and all the variables

64p^2+2p=0

a = 64; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·64·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*64}=\frac{-4}{128}
=-1/32
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*64}=\frac{0}{128}
=0
$