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

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

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

We multiply parentheses ..

(+20x^2-12x-15x+9)=0

We get rid of parentheses

20x^2-12x-15x+9=0

We add all the numbers together, and all the variables

20x^2-27x+9=0

a = 20; b = -27; c = +9;
Δ = b2-4ac
Δ = -272-4·20·9
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3}{2*20}=\frac{24}{40}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3}{2*20}=\frac{30}{40}
=3/4
$