7(y+8)7y+19=0

Solution for 7(y+8)7y+19=0 equation:

7(y+8)7y+19=0

We multiply parentheses

49y^2+392y+19=0

a = 49; b = 392; c = +19;
Δ = b2-4ac
Δ = 3922-4·49·19
Δ = 149940
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:

$\sqrt{\Delta}=\sqrt{149940}=\sqrt{1764*85}=\sqrt{1764}*\sqrt{85}=42\sqrt{85}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(392)-42\sqrt{85}}{2*49}=\frac{-392-42\sqrt{85}}{98}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(392)+42\sqrt{85}}{2*49}=\frac{-392+42\sqrt{85}}{98}
$