(-8x-1)(3x-4)=0

Solution for (-8x-1)(3x-4)=0 equation:

(-8x-1)(3x-4)=0

We multiply parentheses ..

(-24x^2+32x-3x+4)=0

We get rid of parentheses

-24x^2+32x-3x+4=0

We add all the numbers together, and all the variables

-24x^2+29x+4=0

a = -24; b = 29; c = +4;
Δ = b2-4ac
Δ = 292-4·(-24)·4
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-35}{2*-24}=\frac{-64}{-48}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+35}{2*-24}=\frac{6}{-48}
=-1/8
$