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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((-1x^2+9x+2x-18))+x=0


We calculate terms in parentheses: -((-1x^2+9x+2x-18)), so:

(-1x^2+9x+2x-18)

We get rid of parentheses

-1x^2+9x+2x-18

We add all the numbers together, and all the variables

-1x^2+11x-18

Back to the equation:

-(-1x^2+11x-18)


We get rid of parentheses

1x^2-11x+x+18=0

We add all the numbers together, and all the variables

x^2-10x+18=0

a = 1; b = -10; c = +18;
Δ = b2-4ac
Δ = -102-4·1·18
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{7}}{2*1}=\frac{10-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{7}}{2*1}=\frac{10+2\sqrt{7}}{2}
$