.8p-4=2/3p

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

.8p-4=2/3p

We move all terms to the left:

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


Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


(.8p)*3p-4*3p-2=0

We add all the numbers together, and all the variables

(+.8p)*3p-4*3p-2=0

We multiply parentheses

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

Wy multiply elements

3p^2-12p-2=0

a = 3; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·3·(-2)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{42}}{2*3}=\frac{12-2\sqrt{42}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{42}}{2*3}=\frac{12+2\sqrt{42}}{6}
$