(y+1)(y+2)=2(y+7)

Solution for (y+1)(y+2)=2(y+7) equation:

(y+1)(y+2)=2(y+7)

We move all terms to the left:

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

We multiply parentheses ..

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


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

2(y+7)

We multiply parentheses

2y+14

Back to the equation:

-(2y+14)


We get rid of parentheses

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

We add all the numbers together, and all the variables

y^2+y-12=0

a = 1; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·1·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*1}=\frac{-8}{2}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*1}=\frac{6}{2}
=3
$