F(x)=(x*3)-(3x^2)-144x+432

Solution for F(x)=(x*3)-(3x^2)-144x+432 equation:

(F)=(F*3)-(3F^2)-144F+432

We move all terms to the left:

(F)-((F*3)-(3F^2)-144F+432)=0

determiningTheFunctionDomain
-((F*3)-3F^2-144F+432)+F=0

We add all the numbers together, and all the variables

-((+F*3)-3F^2-144F+432)+F=0


We calculate terms in parentheses: -((+F*3)-3F^2-144F+432), so:

(+F*3)-3F^2-144F+432

determiningTheFunctionDomain
-3F^2+(+F*3)-144F+432

We add all the numbers together, and all the variables

-3F^2-144F+(+F*3)+432

We get rid of parentheses

-3F^2-144F+F*3+432

Wy multiply elements

-3F^2-144F+3F+432

We add all the numbers together, and all the variables

-3F^2-141F+432

Back to the equation:

-(-3F^2-141F+432)


We get rid of parentheses

3F^2+141F+F-432=0

We add all the numbers together, and all the variables

3F^2+142F-432=0

a = 3; b = 142; c = -432;
Δ = b2-4ac
Δ = 1422-4·3·(-432)
Δ = 25348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{25348}=\sqrt{4*6337}=\sqrt{4}*\sqrt{6337}=2\sqrt{6337}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(142)-2\sqrt{6337}}{2*3}=\frac{-142-2\sqrt{6337}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(142)+2\sqrt{6337}}{2*3}=\frac{-142+2\sqrt{6337}}{6}
$