X^2+9y^2=16

Solution for X^2+9y^2=16 equation:

X^2+9X^2=16

We move all terms to the left:

X^2+9X^2-(16)=0

We add all the numbers together, and all the variables

10X^2-16=0

a = 10; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·10·(-16)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*10}=\frac{0-8\sqrt{10}}{20}
=-\frac{8\sqrt{10}}{20}
=-\frac{2\sqrt{10}}{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*10}=\frac{0+8\sqrt{10}}{20}
=\frac{8\sqrt{10}}{20}
=\frac{2\sqrt{10}}{5}
$