(y+3)(y+3)=2y(y+7)

Solution for (y+3)(y+3)=2y(y+7) equation:

(y+3)(y+3)=2y(y+7)

We move all terms to the left:

(y+3)(y+3)-(2y(y+7))=0

We multiply parentheses ..

(+y^2+3y+3y+9)-(2y(y+7))=0


We calculate terms in parentheses: -(2y(y+7)), so:

2y(y+7)

We multiply parentheses

2y^2+14y

Back to the equation:

-(2y^2+14y)


We get rid of parentheses

y^2-2y^2+3y+3y-14y+9=0

We add all the numbers together, and all the variables

-1y^2-8y+9=0

a = -1; b = -8; c = +9;
Δ = b2-4ac
Δ = -82-4·(-1)·9
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{-(-8)-10}{2*-1}=\frac{-2}{-2}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*-1}=\frac{18}{-2}
=-9
$