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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -32; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·(-32)·9
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36}{2*-32}=\frac{-24}{-64}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36}{2*-32}=\frac{48}{-64}
=-3/4
$