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

Solution for 3(2x-1)(2x-1)-12=4x+3 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

3(+4x^2-2x-2x+1)-4x-15=0

We multiply parentheses

12x^2-6x-6x-4x+3-15=0

We add all the numbers together, and all the variables

12x^2-16x-12=0

a = 12; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·12·(-12)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{13}}{2*12}=\frac{16-8\sqrt{13}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{13}}{2*12}=\frac{16+8\sqrt{13}}{24}
$