x(x+10)=550

Solution for x(x+10)=550 equation:

x(x+10)=550

We move all terms to the left:

x(x+10)-(550)=0

We multiply parentheses

x^2+10x-550=0

a = 1; b = 10; c = -550;
Δ = b2-4ac
Δ = 102-4·1·(-550)
Δ = 2300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{23}}{2*1}=\frac{-10-10\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{23}}{2*1}=\frac{-10+10\sqrt{23}}{2}
$