(y2+6y)2+14(y2+6y)+45=0

Solution for (y2+6y)2+14(y2+6y)+45=0 equation:

(y2+6y)2+14(y2+6y)+45=0

We add all the numbers together, and all the variables

(+y^2+6y)2+14(+y^2+6y)+45=0

We multiply parentheses

2y^2+14y^2+12y+84y+45=0

We add all the numbers together, and all the variables

16y^2+96y+45=0

a = 16; b = 96; c = +45;
Δ = b2-4ac
Δ = 962-4·16·45
Δ = 6336
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:

$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-24\sqrt{11}}{2*16}=\frac{-96-24\sqrt{11}}{32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+24\sqrt{11}}{2*16}=\frac{-96+24\sqrt{11}}{32}
$