P^3-p^2+(4/27)=0

Solution for P^3-p^2+(4/27)=0 equation:

^3-P^2+(4/27)=0

We add all the numbers together, and all the variables

-P^2+^3+(+4/27)=0

We add all the numbers together, and all the variables

-1P^2+(+4/27)=0

We get rid of parentheses

-1P^2+4/27=0

We multiply all the terms by the denominator


-1P^2*27+4=0

Wy multiply elements

-27P^2+4=0

a = -27; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-27)·4
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-27}=\frac{0-12\sqrt{3}}{-54}
=-\frac{12\sqrt{3}}{-54}
=-\frac{2\sqrt{3}}{-9}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-27}=\frac{0+12\sqrt{3}}{-54}
=\frac{12\sqrt{3}}{-54}
=\frac{2\sqrt{3}}{-9}
$