2y(11+4y)=-7

Solution for 2y(11+4y)=-7 equation:

2y(11+4y)=-7

We move all terms to the left:

2y(11+4y)-(-7)=0

We add all the numbers together, and all the variables

2y(4y+11)-(-7)=0

We add all the numbers together, and all the variables

2y(4y+11)+7=0

We multiply parentheses

8y^2+22y+7=0

a = 8; b = 22; c = +7;
Δ = b2-4ac
Δ = 222-4·8·7
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{65}}{2*8}=\frac{-22-2\sqrt{65}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{65}}{2*8}=\frac{-22+2\sqrt{65}}{16}
$