4x^2-24x=12

Solution for 4x^2-24x=12 equation:

4x^2-24x=12

We move all terms to the left:

4x^2-24x-(12)=0

a = 4; b = -24; c = -12;
Δ = b2-4ac
Δ = -242-4·4·(-12)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{3}}{2*4}=\frac{24-16\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{3}}{2*4}=\frac{24+16\sqrt{3}}{8}
$