3x(4x-3)=12

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

3x(4x-3)=12

We move all terms to the left:

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

We multiply parentheses

12x^2-9x-12=0

a = 12; b = -9; c = -12;
Δ = b2-4ac
Δ = -92-4·12·(-12)
Δ = 657
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{73}}{2*12}=\frac{9-3\sqrt{73}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{73}}{2*12}=\frac{9+3\sqrt{73}}{24}
$