8p-4/3p=2

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

8p-4/3p=2

We move all terms to the left:

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


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We multiply all the terms by the denominator


8p*3p-2*3p-4=0

Wy multiply elements

24p^2-6p-4=0

a = 24; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·24·(-4)
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{105}}{2*24}=\frac{6-2\sqrt{105}}{48}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{105}}{2*24}=\frac{6+2\sqrt{105}}{48}
$