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

We add all the numbers together, and all the variables

4x^2-24x+12=0

a = 4; b = -24; c = +12;
Δ = b2-4ac
Δ = -242-4·4·12
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{6}}{2*4}=\frac{24-8\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{6}}{2*4}=\frac{24+8\sqrt{6}}{8}
$