2y(y+4)=19

Solution for 2y(y+4)=19 equation:

2y(y+4)=19

We move all terms to the left:

2y(y+4)-(19)=0

We multiply parentheses

2y^2+8y-19=0

a = 2; b = 8; c = -19;
Δ = b2-4ac
Δ = 82-4·2·(-19)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{6}}{2*2}=\frac{-8-6\sqrt{6}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{6}}{2*2}=\frac{-8+6\sqrt{6}}{4}
$