2w^2+18w=-3

Solution for 2w^2+18w=-3 equation:

2w^2+18w=-3

We move all terms to the left:

2w^2+18w-(-3)=0

We add all the numbers together, and all the variables

2w^2+18w+3=0

a = 2; b = 18; c = +3;
Δ = b2-4ac
Δ = 182-4·2·3
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10\sqrt{3}}{2*2}=\frac{-18-10\sqrt{3}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10\sqrt{3}}{2*2}=\frac{-18+10\sqrt{3}}{4}
$