(x-4)(9x-3)=0

Solution for (x-4)(9x-3)=0 equation:

(x-4)(9x-3)=0

We multiply parentheses ..

(+9x^2-3x-36x+12)=0

We get rid of parentheses

9x^2-3x-36x+12=0

We add all the numbers together, and all the variables

9x^2-39x+12=0

a = 9; b = -39; c = +12;
Δ = b2-4ac
Δ = -392-4·9·12
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-33}{2*9}=\frac{6}{18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+33}{2*9}=\frac{72}{18}
=4
$