w(2w+5)=133

Solution for w(2w+5)=133 equation:

w(2w+5)=133

We move all terms to the left:

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

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