(1-4x)(3+2x)=0

Solution for (1-4x)(3+2x)=0 equation:

(1-4x)(3+2x)=0

We add all the numbers together, and all the variables

(-4x+1)(2x+3)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-8x^2-10x+3=0

a = -8; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·(-8)·3
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*-8}=\frac{-4}{-16}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*-8}=\frac{24}{-16}
=-1+1/2
$