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

Solution for 3(x+4)(6x-1)=0 equation:

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

We multiply parentheses ..

3(+6x^2-1x+24x-4)=0

We multiply parentheses

18x^2-3x+72x-12=0

We add all the numbers together, and all the variables

18x^2+69x-12=0

a = 18; b = 69; c = -12;
Δ = b2-4ac
Δ = 692-4·18·(-12)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-75}{2*18}=\frac{-144}{36}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+75}{2*18}=\frac{6}{36}
=1/6
$