(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{-6}{24}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+35}{2*12}=\frac{64}{24}
=2+2/3
$