(y+4)(y+7)=9

Solution for (y+4)(y+7)=9 equation:

(y+4)(y+7)=9

We move all terms to the left:

(y+4)(y+7)-(9)=0

We multiply parentheses ..

(+y^2+7y+4y+28)-9=0

We get rid of parentheses

y^2+7y+4y+28-9=0

We add all the numbers together, and all the variables

y^2+11y+19=0

a = 1; b = 11; c = +19;
Δ = b2-4ac
Δ = 112-4·1·19
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{5}}{2*1}=\frac{-11-3\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{5}}{2*1}=\frac{-11+3\sqrt{5}}{2}
$