(9-x)(3x-1)=0

Solution for (9-x)(3x-1)=0 equation:

(9-x)(3x-1)=0

We add all the numbers together, and all the variables

(-1x+9)(3x-1)=0

We multiply parentheses ..

(-3x^2+x+27x-9)=0

We get rid of parentheses

-3x^2+x+27x-9=0

We add all the numbers together, and all the variables

-3x^2+28x-9=0

a = -3; b = 28; c = -9;
Δ = b2-4ac
Δ = 282-4·(-3)·(-9)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-26}{2*-3}=\frac{-54}{-6}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+26}{2*-3}=\frac{-2}{-6}
=1/3
$