2y(16y+9)=5

Solution for 2y(16y+9)=5 equation:

2y(16y+9)=5

We move all terms to the left:

2y(16y+9)-(5)=0

We multiply parentheses

32y^2+18y-5=0

a = 32; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·32·(-5)
Δ = 964
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:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{241}}{2*32}=\frac{-18-2\sqrt{241}}{64}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{241}}{2*32}=\frac{-18+2\sqrt{241}}{64}
$