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

Solution for (10-x)(3x-9)=0 equation:

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

We add all the numbers together, and all the variables

(-1x+10)(3x-9)=0

We multiply parentheses ..

(-3x^2+9x+30x-90)=0

We get rid of parentheses

-3x^2+9x+30x-90=0

We add all the numbers together, and all the variables

-3x^2+39x-90=0

a = -3; b = 39; c = -90;
Δ = b2-4ac
Δ = 392-4·(-3)·(-90)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-21}{2*-3}=\frac{-60}{-6}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+21}{2*-3}=\frac{-18}{-6}
=+3
$