(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^2-11x+15=0

a = -12; b = -11; c = +15;
Δ = b2-4ac
Δ = -112-4·(-12)·15
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-29}{2*-12}=\frac{-18}{-24}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+29}{2*-12}=\frac{40}{-24}
=-1+2/3
$