(y^2+6)-2(8+y)=53

Solution for (y^2+6)-2(8+y)=53 equation:

(y^2+6)-2(8+y)=53

We move all terms to the left:

(y^2+6)-2(8+y)-(53)=0

We add all the numbers together, and all the variables

(y^2+6)-2(y+8)-53=0

We multiply parentheses

(y^2+6)-2y-16-53=0

We get rid of parentheses

y^2-2y+6-16-53=0

We add all the numbers together, and all the variables

y^2-2y-63=0

a = 1; b = -2; c = -63;
Δ = b2-4ac
Δ = -22-4·1·(-63)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-16}{2*1}=\frac{-14}{2}
=-7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+16}{2*1}=\frac{18}{2}
=9
$