54=4x+5x(x+2x)+12+2x

Solution for 54=4x+5x(x+2x)+12+2x equation:

54=4x+5x(x+2x)+12+2x

We move all terms to the left:

54-(4x+5x(x+2x)+12+2x)=0

We add all the numbers together, and all the variables

-(4x+5x(+3x)+12+2x)+54=0


We calculate terms in parentheses: -(4x+5x(+3x)+12+2x), so:

4x+5x(+3x)+12+2x

determiningTheFunctionDomain
4x+5x(+3x)+2x+12

We add all the numbers together, and all the variables

6x+5x(+3x)+12

We multiply parentheses

15x^2+6x+12

Back to the equation:

-(15x^2+6x+12)


We get rid of parentheses

-15x^2-6x-12+54=0

We add all the numbers together, and all the variables

-15x^2-6x+42=0

a = -15; b = -6; c = +42;
Δ = b2-4ac
Δ = -62-4·(-15)·42
Δ = 2556
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:

$\sqrt{\Delta}=\sqrt{2556}=\sqrt{36*71}=\sqrt{36}*\sqrt{71}=6\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{71}}{2*-15}=\frac{6-6\sqrt{71}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{71}}{2*-15}=\frac{6+6\sqrt{71}}{-30}
$