(s-7)s=228

Solution for (s-7)s=228 equation:

(s-7)s=228

We move all terms to the left:

(s-7)s-(228)=0

We multiply parentheses

s^2-7s-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:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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