(2+y)(2+y)=100-y^2

Solution for (2+y)(2+y)=100-y^2 equation:

(2+y)(2+y)=100-y^2

We move all terms to the left:

(2+y)(2+y)-(100-y^2)=0

We add all the numbers together, and all the variables

-(100-y^2)+(y+2)(y+2)=0

We get rid of parentheses

y^2+(y+2)(y+2)-100=0

We multiply parentheses ..

y^2+(+y^2+2y+2y+4)-100=0

We get rid of parentheses

y^2+y^2+2y+2y+4-100=0

We add all the numbers together, and all the variables

2y^2+4y-96=0

a = 2; b = 4; c = -96;
Δ = b2-4ac
Δ = 42-4·2·(-96)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-28}{2*2}=\frac{-32}{4}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+28}{2*2}=\frac{24}{4}
=6
$