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

Solution for 3(x-1)(4x+3)-2(x+6)=0 equation:

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

We multiply parentheses

3(x-1)(4x+3)-2x-12=0

We multiply parentheses ..

3(+4x^2+3x-4x-3)-2x-12=0

We multiply parentheses

12x^2+9x-12x-2x-9-12=0

We add all the numbers together, and all the variables

12x^2-5x-21=0

a = 12; b = -5; c = -21;
Δ = b2-4ac
Δ = -52-4·12·(-21)
Δ = 1033
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{1033}}{2*12}=\frac{5-\sqrt{1033}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1033}}{2*12}=\frac{5+\sqrt{1033}}{24}
$