(3x+2)(4-5x)=0

Solution for (3x+2)(4-5x)=0 equation:

(3x+2)(4-5x)=0

We add all the numbers together, and all the variables

(3x+2)(-5x+4)=0

We multiply parentheses ..

(-15x^2+12x-10x+8)=0

We get rid of parentheses

-15x^2+12x-10x+8=0

We add all the numbers together, and all the variables

-15x^2+2x+8=0

a = -15; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-15)·8
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*-15}=\frac{-24}{-30}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*-15}=\frac{20}{-30}
=-2/3
$