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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-15x^2+12x-25x+20)=0

We get rid of parentheses

-15x^2+12x-25x+20=0

We add all the numbers together, and all the variables

-15x^2-13x+20=0

a = -15; b = -13; c = +20;
Δ = b2-4ac
Δ = -132-4·(-15)·20
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-37}{2*-15}=\frac{-24}{-30}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+37}{2*-15}=\frac{50}{-30}
=-1+2/3
$