7/4p-3=2+4/8p

Solution for 7/4p-3=2+4/8p equation:

7/4p-3=2+4/8p

We move all terms to the left:

7/4p-3-(2+4/8p)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 8p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

7/4p-(4/8p+2)-3=0

We get rid of parentheses

7/4p-4/8p-2-3=0

We calculate fractions


56p/32p^2+(-16p)/32p^2-2-3=0

We add all the numbers together, and all the variables

56p/32p^2+(-16p)/32p^2-5=0

We multiply all the terms by the denominator


56p+(-16p)-5*32p^2=0

Wy multiply elements

-160p^2+56p+(-16p)=0

We get rid of parentheses

-160p^2+56p-16p=0

We add all the numbers together, and all the variables

-160p^2+40p=0

a = -160; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-160)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-160}=\frac{-80}{-320}
=1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-160}=\frac{0}{-320}
=0
$