12x^2-48x=-0.5

Solution for 12x^2-48x=-0.5 equation:

12x^2-48x=-0.5

We move all terms to the left:

12x^2-48x-(-0.5)=0

We add all the numbers together, and all the variables

12x^2-48x+0.5=0

a = 12; b = -48; c = +0.5;
Δ = b2-4ac
Δ = -482-4·12·0.5
Δ = 2280
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:

$\sqrt{\Delta}=\sqrt{2280}=\sqrt{4*570}=\sqrt{4}*\sqrt{570}=2\sqrt{570}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{570}}{2*12}=\frac{48-2\sqrt{570}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{570}}{2*12}=\frac{48+2\sqrt{570}}{24}
$