(-y-7)(-y-7)+y^2=49

Solution for (-y-7)(-y-7)+y^2=49 equation:

(-y-7)(-y-7)+y^2=49

We move all terms to the left:

(-y-7)(-y-7)+y^2-(49)=0

We add all the numbers together, and all the variables

y^2+(-1y-7)(-1y-7)-49=0

We multiply parentheses ..

y^2+(+y^2+7y+7y+49)-49=0

We get rid of parentheses

y^2+y^2+7y+7y+49-49=0

We add all the numbers together, and all the variables

2y^2+14y=0

a = 2; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·2·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*2}=\frac{-28}{4}
=-7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*2}=\frac{0}{4}
=0
$