2y(16y+9)=15-12+54

Solution for 2y(16y+9)=15-12+54 equation:

2y(16y+9)=15-12+54

We move all terms to the left:

2y(16y+9)-(15-12+54)=0

We add all the numbers together, and all the variables

2y(16y+9)-57=0

We multiply parentheses

32y^2+18y-57=0

a = 32; b = 18; c = -57;
Δ = b2-4ac
Δ = 182-4·32·(-57)
Δ = 7620
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:

$\sqrt{\Delta}=\sqrt{7620}=\sqrt{4*1905}=\sqrt{4}*\sqrt{1905}=2\sqrt{1905}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{1905}}{2*32}=\frac{-18-2\sqrt{1905}}{64}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{1905}}{2*32}=\frac{-18+2\sqrt{1905}}{64}
$