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

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

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