X^2-9y^2=-35

Solution for X^2-9y^2=-35 equation:

X^2-9X^2=-35

We move all terms to the left:

X^2-9X^2-(-35)=0

We add all the numbers together, and all the variables

-8X^2+35=0

a = -8; b = 0; c = +35;
Δ = b2-4ac
Δ = 02-4·(-8)·35
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{70}}{2*-8}=\frac{0-4\sqrt{70}}{-16}
=-\frac{4\sqrt{70}}{-16}
=-\frac{\sqrt{70}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{70}}{2*-8}=\frac{0+4\sqrt{70}}{-16}
=\frac{4\sqrt{70}}{-16}
=\frac{\sqrt{70}}{-4}
$