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

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

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

We multiply parentheses ..

(+32x^2-4x+8x-1)=0

We get rid of parentheses

32x^2-4x+8x-1=0

We add all the numbers together, and all the variables

32x^2+4x-1=0

a = 32; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·32·(-1)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*32}=\frac{-16}{64}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*32}=\frac{8}{64}
=1/8
$