w(w+4.75)=133.5

Solution for w(w+4.75)=133.5 equation:

w(w+4.75)=133.5

We move all terms to the left:

w(w+4.75)-(133.5)=0

We add all the numbers together, and all the variables

w(w+4.75)-133.5=0

We multiply parentheses

w^2+4.75w-133.5=0

a = 1; b = 4.75; c = -133.5;
Δ = b2-4ac
Δ = 4.752-4·1·(-133.5)
Δ = 556.5625
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{-(4.75)-\sqrt{556.5625}}{2*1}=\frac{-4.75-\sqrt{556.5625}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.75)+\sqrt{556.5625}}{2*1}=\frac{-4.75+\sqrt{556.5625}}{2}
$