-9=6x(2-x)

Solution for -9=6x(2-x) equation:

-9=6x(2-x)

We move all terms to the left:

-9-(6x(2-x))=0

We add all the numbers together, and all the variables

-(6x(-1x+2))-9=0


We calculate terms in parentheses: -(6x(-1x+2)), so:

6x(-1x+2)

We multiply parentheses

-6x^2+12x

Back to the equation:

-(-6x^2+12x)


We get rid of parentheses

6x^2-12x-9=0

a = 6; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·6·(-9)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{10}}{2*6}=\frac{12-6\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{10}}{2*6}=\frac{12+6\sqrt{10}}{12}
$