9-3x(x-2)=x-9

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

9-3x(x-2)=x-9

We move all terms to the left:

9-3x(x-2)-(x-9)=0

We multiply parentheses

-3x^2+6x-(x-9)+9=0

We get rid of parentheses

-3x^2+6x-x+9+9=0

We add all the numbers together, and all the variables

-3x^2+5x+18=0

a = -3; b = 5; c = +18;
Δ = b2-4ac
Δ = 52-4·(-3)·18
Δ = 241
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{-(5)-\sqrt{241}}{2*-3}=\frac{-5-\sqrt{241}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{241}}{2*-3}=\frac{-5+\sqrt{241}}{-6}
$