44-9x=12-5x(2x-7)

Solution for 44-9x=12-5x(2x-7) equation:

44-9x=12-5x(2x-7)

We move all terms to the left:

44-9x-(12-5x(2x-7))=0


We calculate terms in parentheses: -(12-5x(2x-7)), so:

12-5x(2x-7)

determiningTheFunctionDomain
-5x(2x-7)+12

We multiply parentheses

-10x^2+35x+12

Back to the equation:

-(-10x^2+35x+12)


We get rid of parentheses

10x^2-35x-9x-12+44=0

We add all the numbers together, and all the variables

10x^2-44x+32=0

a = 10; b = -44; c = +32;
Δ = b2-4ac
Δ = -442-4·10·32
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{41}}{2*10}=\frac{44-4\sqrt{41}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{41}}{2*10}=\frac{44+4\sqrt{41}}{20}
$