Y^2+x^2+8x=84

Solution for Y^2+x^2+8x=84 equation:

^2+Y^2+8Y=84

We move all terms to the left:

^2+Y^2+8Y-(84)=0

determiningTheFunctionDomain
Y^2+8Y-84+^2=0

We add all the numbers together, and all the variables

Y^2+8Y=0

a = 1; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·1·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*1}=\frac{-16}{2}
=-8
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*1}=\frac{0}{2}
=0
$