4x^2-16x-48=12

Solution for 4x^2-16x-48=12 equation:

4x^2-16x-48=12

We move all terms to the left:

4x^2-16x-48-(12)=0

We add all the numbers together, and all the variables

4x^2-16x-60=0

a = 4; b = -16; c = -60;
Δ = b2-4ac
Δ = -162-4·4·(-60)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{19}}{2*4}=\frac{16-8\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{19}}{2*4}=\frac{16+8\sqrt{19}}{8}
$