w(w+2.2)-4w=9.3

Solution for w(w+2.2)-4w=9.3 equation:

w(w+2.2)-4w=9.3

We move all terms to the left:

w(w+2.2)-4w-(9.3)=0

We add all the numbers together, and all the variables

-4w+w(w+2.2)-9.3=0

We multiply parentheses

w^2-4w+2.2w-9.3=0

We add all the numbers together, and all the variables

w^2-1.8w-9.3=0

a = 1; b = -1.8; c = -9.3;
Δ = b2-4ac
Δ = -1.82-4·1·(-9.3)
Δ = 40.44
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{-(-1.8)-\sqrt{40.44}}{2*1}=\frac{1.8-\sqrt{40.44}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.8)+\sqrt{40.44}}{2*1}=\frac{1.8+\sqrt{40.44}}{2}
$