2(y+7)y=4

Solution for 2(y+7)y=4 equation:

2(y+7)y=4

We move all terms to the left:

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

We multiply parentheses

2y^2+14y-4=0

a = 2; b = 14; c = -4;
Δ = b2-4ac
Δ = 142-4·2·(-4)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{57}}{2*2}=\frac{-14-2\sqrt{57}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{57}}{2*2}=\frac{-14+2\sqrt{57}}{4}
$