3w^2-18w^2+9w+30=0

Solution for 3w^2-18w^2+9w+30=0 equation:

3w^2-18w^2+9w+30=0

We add all the numbers together, and all the variables

-15w^2+9w+30=0

a = -15; b = 9; c = +30;
Δ = b2-4ac
Δ = 92-4·(-15)·30
Δ = 1881
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:

$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{209}}{2*-15}=\frac{-9-3\sqrt{209}}{-30}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{209}}{2*-15}=\frac{-9+3\sqrt{209}}{-30}
$