4x^2-3=12x

Solution for 4x^2-3=12x equation:

4x^2-3=12x

We move all terms to the left:

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

a = 4; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·4·(-3)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*4}=\frac{12-8\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*4}=\frac{12+8\sqrt{3}}{8}
$