3(2/3)p=11

Solution for 3(2/3)p=11 equation:

3(2/3)p=11

We move all terms to the left:

3(2/3)p-(11)=0


Domain of the equation: 3)p!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

3(+2/3)p-11=0

We multiply parentheses

6p^2-11=0

a = 6; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·6·(-11)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*6}=\frac{0-2\sqrt{66}}{12}
=-\frac{2\sqrt{66}}{12}
=-\frac{\sqrt{66}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*6}=\frac{0+2\sqrt{66}}{12}
=\frac{2\sqrt{66}}{12}
=\frac{\sqrt{66}}{6}
$