X^2-21y^2=-12

Solution for X^2-21y^2=-12 equation:

X^2-21X^2=-12

We move all terms to the left:

X^2-21X^2-(-12)=0

We add all the numbers together, and all the variables

-20X^2+12=0

a = -20; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-20)·12
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*-20}=\frac{0-8\sqrt{15}}{-40}
=-\frac{8\sqrt{15}}{-40}
=-\frac{\sqrt{15}}{-5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*-20}=\frac{0+8\sqrt{15}}{-40}
=\frac{8\sqrt{15}}{-40}
=\frac{\sqrt{15}}{-5}
$