2x=54-18x+8x(x+12)

Solution for 2x=54-18x+8x(x+12) equation:

2x=54-18x+8x(x+12)

We move all terms to the left:

2x-(54-18x+8x(x+12))=0


We calculate terms in parentheses: -(54-18x+8x(x+12)), so:

54-18x+8x(x+12)

determiningTheFunctionDomain
-18x+8x(x+12)+54

We multiply parentheses

8x^2-18x+96x+54

We add all the numbers together, and all the variables

8x^2+78x+54

Back to the equation:

-(8x^2+78x+54)


We get rid of parentheses

-8x^2+2x-78x-54=0

We add all the numbers together, and all the variables

-8x^2-76x-54=0

a = -8; b = -76; c = -54;
Δ = b2-4ac
Δ = -762-4·(-8)·(-54)
Δ = 4048
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4048}=\sqrt{16*253}=\sqrt{16}*\sqrt{253}=4\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{253}}{2*-8}=\frac{76-4\sqrt{253}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{253}}{2*-8}=\frac{76+4\sqrt{253}}{-16}
$