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

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

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

We move all terms to the left:

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


Domain of the equation: 4p-3)!=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

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

We multiply parentheses

56p-(8(4/8p+2))-24=0

We multiply all the terms by the denominator


56p*8p-24*8p+2))-(8(4+2))=0

We add all the numbers together, and all the variables

56p*8p-24*8p+2))-(86)=0

We add all the numbers together, and all the variables

56p*8p-24*8p=0

Wy multiply elements

448p^2-192p=0

a = 448; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·448·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-192}{2*448}=\frac{0}{896}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*448}=\frac{384}{896}
=3/7
$