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

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

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

We multiply parentheses ..

(+12x^2+32x-9x-24)=0

We get rid of parentheses

12x^2+32x-9x-24=0

We add all the numbers together, and all the variables

12x^2+23x-24=0

a = 12; b = 23; c = -24;
Δ = b2-4ac
Δ = 232-4·12·(-24)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-41}{2*12}=\frac{-64}{24}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+41}{2*12}=\frac{18}{24}
=3/4
$