(w)(7+w)=228

Solution for (w)(7+w)=228 equation:

(w)(7+w)=228

We move all terms to the left:

(w)(7+w)-(228)=0

We add all the numbers together, and all the variables

w(w+7)-228=0

We multiply parentheses

w^2+7w-228=0

a = 1; b = 7; c = -228;
Δ = b2-4ac
Δ = 72-4·1·(-228)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-31}{2*1}=\frac{-38}{2}
=-19
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+31}{2*1}=\frac{24}{2}
=12
$