7y(y+7)=-56

Solution for 7y(y+7)=-56 equation:

7y(y+7)=-56

We move all terms to the left:

7y(y+7)-(-56)=0

We add all the numbers together, and all the variables

7y(y+7)+56=0

We multiply parentheses

7y^2+49y+56=0

a = 7; b = 49; c = +56;
Δ = b2-4ac
Δ = 492-4·7·56
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-7\sqrt{17}}{2*7}=\frac{-49-7\sqrt{17}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+7\sqrt{17}}{2*7}=\frac{-49+7\sqrt{17}}{14}
$