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

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

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

We multiply parentheses

4x^2-12x+3x-9=0

We add all the numbers together, and all the variables

4x^2-9x-9=0

a = 4; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·4·(-9)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*4}=\frac{-6}{8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*4}=\frac{24}{8}
=3
$