X^2+y^2=61/4

Solution for X^2+y^2=61/4 equation:

X^2+X^2=61/4

We move all terms to the left:

X^2+X^2-(61/4)=0

We add all the numbers together, and all the variables

X^2+X^2-(+61/4)=0

We add all the numbers together, and all the variables

2X^2-(+61/4)=0

We get rid of parentheses

2X^2-61/4=0

We multiply all the terms by the denominator


2X^2*4-61=0

Wy multiply elements

8X^2-61=0

a = 8; b = 0; c = -61;
Δ = b2-4ac
Δ = 02-4·8·(-61)
Δ = 1952
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:

$\sqrt{\Delta}=\sqrt{1952}=\sqrt{16*122}=\sqrt{16}*\sqrt{122}=4\sqrt{122}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{122}}{2*8}=\frac{0-4\sqrt{122}}{16}
=-\frac{4\sqrt{122}}{16}
=-\frac{\sqrt{122}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{122}}{2*8}=\frac{0+4\sqrt{122}}{16}
=\frac{4\sqrt{122}}{16}
=\frac{\sqrt{122}}{4}
$