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

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

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

We multiply parentheses ..

(+12x^2+32x-3x-8)=0

We get rid of parentheses

12x^2+32x-3x-8=0

We add all the numbers together, and all the variables

12x^2+29x-8=0

a = 12; b = 29; c = -8;
Δ = b2-4ac
Δ = 292-4·12·(-8)
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*12}=\frac{-64}{24}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+35}{2*12}=\frac{6}{24}
=1/4
$