(3x-12)(4x+1)=0

Solution for (3x-12)(4x+1)=0 equation:

(3x-12)(4x+1)=0

We multiply parentheses ..

(+12x^2+3x-48x-12)=0

We get rid of parentheses

12x^2+3x-48x-12=0

We add all the numbers together, and all the variables

12x^2-45x-12=0

a = 12; b = -45; c = -12;
Δ = b2-4ac
Δ = -452-4·12·(-12)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-51}{2*12}=\frac{-6}{24}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+51}{2*12}=\frac{96}{24}
=4
$