(7)/(8)p-(1)/(4)=(1)/(2)p

Solution for (7)/(8)p-(1)/(4)=(1)/(2)p equation:

(7)/(8)p-(1)/(4)=(1)/(2)p

We move all terms to the left:

(7)/(8)p-(1)/(4)-((1)/(2)p)=0


Domain of the equation: 8p!=0

p!=0/8

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

7/8p-(+1/2p)-1/4=0

We get rid of parentheses

7/8p-1/2p-1/4=0

We calculate fractions


(-32p^2)/256p^2+224p/256p^2+(-128p)/256p^2=0

We multiply all the terms by the denominator


(-32p^2)+224p+(-128p)=0

We get rid of parentheses

-32p^2+224p-128p=0

We add all the numbers together, and all the variables

-32p^2+96p=0

a = -32; b = 96; c = 0;
Δ = b2-4ac
Δ = 962-4·(-32)·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-96}{2*-32}=\frac{-192}{-64}
=+3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+96}{2*-32}=\frac{0}{-64}
=0
$