X^2+y^2=144/81=1

Solution for X^2+y^2=144/81=1 equation:

X^2+X^2=144/81=1

We move all terms to the left:

X^2+X^2-(144/81)=0

We add all the numbers together, and all the variables

X^2+X^2-(+144/81)=0

We add all the numbers together, and all the variables

2X^2-(+144/81)=0

We get rid of parentheses

2X^2-144/81=0

We multiply all the terms by the denominator


2X^2*81-144=0

Wy multiply elements

162X^2-144=0

a = 162; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·162·(-144)
Δ = 93312
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:

$\sqrt{\Delta}=\sqrt{93312}=\sqrt{46656*2}=\sqrt{46656}*\sqrt{2}=216\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-216\sqrt{2}}{2*162}=\frac{0-216\sqrt{2}}{324}
=-\frac{216\sqrt{2}}{324}
=-\frac{2\sqrt{2}}{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+216\sqrt{2}}{2*162}=\frac{0+216\sqrt{2}}{324}
=\frac{216\sqrt{2}}{324}
=\frac{2\sqrt{2}}{3}
$