2x(x-3)-44=37-x(6-x)

Solution for 2x(x-3)-44=37-x(6-x) equation:

2x(x-3)-44=37-x(6-x)

We move all terms to the left:

2x(x-3)-44-(37-x(6-x))=0

We add all the numbers together, and all the variables

2x(x-3)-(37-x(-1x+6))-44=0

We multiply parentheses

2x^2-6x-(37-x(-1x+6))-44=0


We calculate terms in parentheses: -(37-x(-1x+6)), so:

37-x(-1x+6)

determiningTheFunctionDomain
-x(-1x+6)+37

We multiply parentheses

1x^2-6x+37

We add all the numbers together, and all the variables

x^2-6x+37

Back to the equation:

-(x^2-6x+37)


We get rid of parentheses

2x^2-x^2-6x+6x-37-44=0

We add all the numbers together, and all the variables

x^2-81=0

a = 1; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·1·(-81)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*1}=\frac{18}{2}
=9
$