12-9x=5-2(3x-2)x+3x

Solution for 12-9x=5-2(3x-2)x+3x equation:

12-9x=5-2(3x-2)x+3x

We move all terms to the left:

12-9x-(5-2(3x-2)x+3x)=0


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

5-2(3x-2)x+3x

determiningTheFunctionDomain
-2(3x-2)x+3x+5

We add all the numbers together, and all the variables

3x-2(3x-2)x+5

We multiply parentheses

-6x^2+3x+4x+5

We add all the numbers together, and all the variables

-6x^2+7x+5

Back to the equation:

-(-6x^2+7x+5)


We get rid of parentheses

6x^2-7x-9x-5+12=0

We add all the numbers together, and all the variables

6x^2-16x+7=0

a = 6; b = -16; c = +7;
Δ = b2-4ac
Δ = -162-4·6·7
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{22}}{2*6}=\frac{16-2\sqrt{22}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{22}}{2*6}=\frac{16+2\sqrt{22}}{12}
$