-2y(-4y+-9)=42

Solution for -2y(-4y+-9)=42 equation:

-2y(-4y+-9)=42

We move all terms to the left:

-2y(-4y+-9)-(42)=0

We add all the numbers together, and all the variables

-2y(-4y-9)-42=0

We multiply parentheses

8y^2+18y-42=0

a = 8; b = 18; c = -42;
Δ = b2-4ac
Δ = 182-4·8·(-42)
Δ = 1668
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:

$\sqrt{\Delta}=\sqrt{1668}=\sqrt{4*417}=\sqrt{4}*\sqrt{417}=2\sqrt{417}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{417}}{2*8}=\frac{-18-2\sqrt{417}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{417}}{2*8}=\frac{-18+2\sqrt{417}}{16}
$