12x^2=1024

Solution for 12x^2=1024 equation:

12x^2=1024

We move all terms to the left:

12x^2-(1024)=0

a = 12; b = 0; c = -1024;
Δ = b2-4ac
Δ = 02-4·12·(-1024)
Δ = 49152
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:

$\sqrt{\Delta}=\sqrt{49152}=\sqrt{16384*3}=\sqrt{16384}*\sqrt{3}=128\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128\sqrt{3}}{2*12}=\frac{0-128\sqrt{3}}{24}
=-\frac{128\sqrt{3}}{24}
=-\frac{16\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128\sqrt{3}}{2*12}=\frac{0+128\sqrt{3}}{24}
=\frac{128\sqrt{3}}{24}
=\frac{16\sqrt{3}}{3}
$