(Y+7)(y+7)=y2

Solution for (Y+7)(y+7)=y2 equation:

(+7)(Y+7)=Y2

We move all terms to the left:

(+7)(Y+7)-(Y2)=0

We add all the numbers together, and all the variables

7(Y+7)-Y2=0

We add all the numbers together, and all the variables

-1Y^2+7(Y+7)=0

We multiply parentheses

-1Y^2+7Y+49=0

a = -1; b = 7; c = +49;
Δ = b2-4ac
Δ = 72-4·(-1)·49
Δ = 245
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7\sqrt{5}}{2*-1}=\frac{-7-7\sqrt{5}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7\sqrt{5}}{2*-1}=\frac{-7+7\sqrt{5}}{-2}
$