3w^2+33w+7=0

Solution for 3w^2+33w+7=0 equation:

3w^2+33w+7=0

a = 3; b = 33; c = +7;
Δ = b2-4ac
Δ = 332-4·3·7
Δ = 1005
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{1005}}{2*3}=\frac{-33-\sqrt{1005}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1005}}{2*3}=\frac{-33+\sqrt{1005}}{6}
$