(3x-1)(4x+16)=0

Solution for (3x-1)(4x+16)=0 equation:

(3x-1)(4x+16)=0

We multiply parentheses ..

(+12x^2+48x-4x-16)=0

We get rid of parentheses

12x^2+48x-4x-16=0

We add all the numbers together, and all the variables

12x^2+44x-16=0

a = 12; b = 44; c = -16;
Δ = b2-4ac
Δ = 442-4·12·(-16)
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*12}=\frac{-96}{24}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+52}{2*12}=\frac{8}{24}
=1/3
$