4y(4+2y)=-6y-10

Solution for 4y(4+2y)=-6y-10 equation:

4y(4+2y)=-6y-10

We move all terms to the left:

4y(4+2y)-(-6y-10)=0

We add all the numbers together, and all the variables

4y(2y+4)-(-6y-10)=0

We multiply parentheses

8y^2+16y-(-6y-10)=0

We get rid of parentheses

8y^2+16y+6y+10=0

We add all the numbers together, and all the variables

8y^2+22y+10=0

a = 8; b = 22; c = +10;
Δ = b2-4ac
Δ = 222-4·8·10
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{41}}{2*8}=\frac{-22-2\sqrt{41}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{41}}{2*8}=\frac{-22+2\sqrt{41}}{16}
$