x=(18-2x)(3-2x)

Solution for x=(18-2x)(3-2x) equation:

x=(18-2x)(3-2x)

We move all terms to the left:

x-((18-2x)(3-2x))=0

We add all the numbers together, and all the variables

x-((-2x+18)(-2x+3))=0

We multiply parentheses ..

-((+4x^2-6x-36x+54))+x=0


We calculate terms in parentheses: -((+4x^2-6x-36x+54)), so:

(+4x^2-6x-36x+54)

We get rid of parentheses

4x^2-6x-36x+54

We add all the numbers together, and all the variables

4x^2-42x+54

Back to the equation:

-(4x^2-42x+54)


We add all the numbers together, and all the variables

x-(4x^2-42x+54)=0

We get rid of parentheses

-4x^2+x+42x-54=0

We add all the numbers together, and all the variables

-4x^2+43x-54=0

a = -4; b = 43; c = -54;
Δ = b2-4ac
Δ = 432-4·(-4)·(-54)
Δ = 985
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{-(43)-\sqrt{985}}{2*-4}=\frac{-43-\sqrt{985}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{985}}{2*-4}=\frac{-43+\sqrt{985}}{-8}
$