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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-12x^2+29x-15=0

a = -12; b = 29; c = -15;
Δ = b2-4ac
Δ = 292-4·(-12)·(-15)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-11}{2*-12}=\frac{-40}{-24}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+11}{2*-12}=\frac{-18}{-24}
=3/4
$