5x(4x-9)+3(4x-9)=0

Solution for 5x(4x-9)+3(4x-9)=0 equation:

5x(4x-9)+3(4x-9)=0

We multiply parentheses

20x^2-45x+12x-27=0

We add all the numbers together, and all the variables

20x^2-33x-27=0

a = 20; b = -33; c = -27;
Δ = b2-4ac
Δ = -332-4·20·(-27)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-57}{2*20}=\frac{-24}{40}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+57}{2*20}=\frac{90}{40}
=2+1/4
$