x^2+4=12x^2

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

x^2+4=12x^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-11x^2+4=0

a = -11; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-11)·4
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{11}}{2*-11}=\frac{0-4\sqrt{11}}{-22}
=-\frac{4\sqrt{11}}{-22}
=-\frac{2\sqrt{11}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{11}}{2*-11}=\frac{0+4\sqrt{11}}{-22}
=\frac{4\sqrt{11}}{-22}
=\frac{2\sqrt{11}}{-11}
$