-7/4p+1/2p=-5/8

Solution for -7/4p+1/2p=-5/8 equation:

-7/4p+1/2p=-5/8

We move all terms to the left:

-7/4p+1/2p-(-5/8)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

-7/4p+1/2p+5/8=0

We calculate fractions


80p^2/512p^2+(-896p)/512p^2+256p/512p^2=0

We multiply all the terms by the denominator


80p^2+(-896p)+256p=0

We add all the numbers together, and all the variables

80p^2+256p+(-896p)=0

We get rid of parentheses

80p^2+256p-896p=0

We add all the numbers together, and all the variables

80p^2-640p=0

a = 80; b = -640; c = 0;
Δ = b2-4ac
Δ = -6402-4·80·0
Δ = 409600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{409600}=640$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-640)-640}{2*80}=\frac{0}{160}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-640)+640}{2*80}=\frac{1280}{160}
=8
$