-2w(2w-9)=-38

Solution for -2w(2w-9)=-38 equation:

-2w(2w-9)=-38

We move all terms to the left:

-2w(2w-9)-(-38)=0

We add all the numbers together, and all the variables

-2w(2w-9)+38=0

We multiply parentheses

-4w^2+18w+38=0

a = -4; b = 18; c = +38;
Δ = b2-4ac
Δ = 182-4·(-4)·38
Δ = 932
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{233}}{2*-4}=\frac{-18-2\sqrt{233}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{233}}{2*-4}=\frac{-18+2\sqrt{233}}{-8}
$