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

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

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

We multiply parentheses ..

(+18x^2+24x-3x-4)=0

We get rid of parentheses

18x^2+24x-3x-4=0

We add all the numbers together, and all the variables

18x^2+21x-4=0

a = 18; b = 21; c = -4;
Δ = b2-4ac
Δ = 212-4·18·(-4)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*18}=\frac{-48}{36}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*18}=\frac{6}{36}
=1/6
$