(8x-1)(4x+6)=0

Solution for (8x-1)(4x+6)=0 equation:

(8x-1)(4x+6)=0

We multiply parentheses ..

(+32x^2+48x-4x-6)=0

We get rid of parentheses

32x^2+48x-4x-6=0

We add all the numbers together, and all the variables

32x^2+44x-6=0

a = 32; b = 44; c = -6;
Δ = b2-4ac
Δ = 442-4·32·(-6)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-52}{2*32}=\frac{-96}{64}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+52}{2*32}=\frac{8}{64}
=1/8
$