X^2-12y^2=-1

Solution for X^2-12y^2=-1 equation:

X^2-12X^2=-1

We move all terms to the left:

X^2-12X^2-(-1)=0

We add all the numbers together, and all the variables

-11X^2+1=0

a = -11; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-11)·1
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{11}}{2*-11}=\frac{0-2\sqrt{11}}{-22}
=-\frac{2\sqrt{11}}{-22}
=-\frac{\sqrt{11}}{-11}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{11}}{2*-11}=\frac{0+2\sqrt{11}}{-22}
=\frac{2\sqrt{11}}{-22}
=\frac{\sqrt{11}}{-11}
$