X^2+9y^2=144

Solution for X^2+9y^2=144 equation:

X^2+9X^2=144

We move all terms to the left:

X^2+9X^2-(144)=0

We add all the numbers together, and all the variables

10X^2-144=0

a = 10; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·10·(-144)
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{10}}{2*10}=\frac{0-24\sqrt{10}}{20}
=-\frac{24\sqrt{10}}{20}
=-\frac{6\sqrt{10}}{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{10}}{2*10}=\frac{0+24\sqrt{10}}{20}
=\frac{24\sqrt{10}}{20}
=\frac{6\sqrt{10}}{5}
$