-18=-34w-4w^2

Solution for -18=-34w-4w^2 equation:

-18=-34w-4w^2

We move all terms to the left:

-18-(-34w-4w^2)=0

We get rid of parentheses

4w^2+34w-18=0

a = 4; b = 34; c = -18;
Δ = b2-4ac
Δ = 342-4·4·(-18)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-38}{2*4}=\frac{-72}{8}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+38}{2*4}=\frac{4}{8}
=1/2
$