-12x+48=4x^2+4

Solution for -12x+48=4x^2+4 equation:

-12x+48=4x^2+4

We move all terms to the left:

-12x+48-(4x^2+4)=0

We get rid of parentheses

-4x^2-12x-4+48=0

We add all the numbers together, and all the variables

-4x^2-12x+44=0

a = -4; b = -12; c = +44;
Δ = b2-4ac
Δ = -122-4·(-4)·44
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{53}}{2*-4}=\frac{12-4\sqrt{53}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{53}}{2*-4}=\frac{12+4\sqrt{53}}{-8}
$