X=18-2x(24-2x)

Solution for X=18-2x(24-2x) equation:

X=18-2X(24-2X)

We move all terms to the left:

X-(18-2X(24-2X))=0

We add all the numbers together, and all the variables

X-(18-2X(-2X+24))=0


We calculate terms in parentheses: -(18-2X(-2X+24)), so:

18-2X(-2X+24)

determiningTheFunctionDomain
-2X(-2X+24)+18

We multiply parentheses

4X^2-48X+18

Back to the equation:

-(4X^2-48X+18)


We get rid of parentheses

-4X^2+X+48X-18=0

We add all the numbers together, and all the variables

-4X^2+49X-18=0

a = -4; b = 49; c = -18;
Δ = b2-4ac
Δ = 492-4·(-4)·(-18)
Δ = 2113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-\sqrt{2113}}{2*-4}=\frac{-49-\sqrt{2113}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{2113}}{2*-4}=\frac{-49+\sqrt{2113}}{-8}
$