p=32/3p+4

Solution for p=32/3p+4 equation:

p=32/3p+4

We move all terms to the left:

p-(32/3p+4)=0


Domain of the equation: 3p+4)!=0

p∈R


We get rid of parentheses

p-32/3p-4=0

We multiply all the terms by the denominator


p*3p-4*3p-32=0

Wy multiply elements

3p^2-12p-32=0

a = 3; b = -12; c = -32;
Δ = b2-4ac
Δ = -122-4·3·(-32)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{33}}{2*3}=\frac{12-4\sqrt{33}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{33}}{2*3}=\frac{12+4\sqrt{33}}{6}
$