(3x+8)(5-4x)=0

Solution for (3x+8)(5-4x)=0 equation:

(3x+8)(5-4x)=0

We add all the numbers together, and all the variables

(3x+8)(-4x+5)=0

We multiply parentheses ..

(-12x^2+15x-32x+40)=0

We get rid of parentheses

-12x^2+15x-32x+40=0

We add all the numbers together, and all the variables

-12x^2-17x+40=0

a = -12; b = -17; c = +40;
Δ = b2-4ac
Δ = -172-4·(-12)·40
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-47}{2*-12}=\frac{-30}{-24}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+47}{2*-12}=\frac{64}{-24}
=-2+2/3
$