(y+6)2+y2=36

Solution for (y+6)2+y2=36 equation:

(y+6)2+y2=36

We move all terms to the left:

(y+6)2+y2-(36)=0

We add all the numbers together, and all the variables

y^2+(y+6)2-36=0

We multiply parentheses

y^2+2y+12-36=0

We add all the numbers together, and all the variables

y^2+2y-24=0

a = 1; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*1}=\frac{-12}{2}
=-6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*1}=\frac{8}{2}
=4
$