X^2+y^2-6=56-8y

Solution for X^2+y^2-6=56-8y equation:

X^2+X^2-6=56-8X

We move all terms to the left:

X^2+X^2-6-(56-8X)=0

We add all the numbers together, and all the variables

X^2+X^2-(-8X+56)-6=0

We add all the numbers together, and all the variables

2X^2-(-8X+56)-6=0

We get rid of parentheses

2X^2+8X-56-6=0

We add all the numbers together, and all the variables

2X^2+8X-62=0

a = 2; b = 8; c = -62;
Δ = b2-4ac
Δ = 82-4·2·(-62)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{35}}{2*2}=\frac{-8-4\sqrt{35}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{35}}{2*2}=\frac{-8+4\sqrt{35}}{4}
$