133=5w+2w^2

Solution for 133=5w+2w^2 equation:

133=5w+2w^2

We move all terms to the left:

133-(5w+2w^2)=0

We get rid of parentheses

-2w^2-5w+133=0

a = -2; b = -5; c = +133;
Δ = b2-4ac
Δ = -52-4·(-2)·133
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-33}{2*-2}=\frac{-28}{-4}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+33}{2*-2}=\frac{38}{-4}
=-9+1/2
$