12x-6x^2=4

Solution for 12x-6x^2=4 equation:

12x-6x^2=4

We move all terms to the left:

12x-6x^2-(4)=0

a = -6; b = 12; c = -4;
Δ = b2-4ac
Δ = 122-4·(-6)·(-4)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{3}}{2*-6}=\frac{-12-4\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{3}}{2*-6}=\frac{-12+4\sqrt{3}}{-12}
$