x(x+7)=228

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

x(x+7)=228

We move all terms to the left:

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

We multiply parentheses

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

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