x(x+50)=2

Solution for x(x+50)=2 equation:

x(x+50)=2

We move all terms to the left:

x(x+50)-(2)=0

We multiply parentheses

x^2+50x-2=0

a = 1; b = 50; c = -2;
Δ = b2-4ac
Δ = 502-4·1·(-2)
Δ = 2508
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:

$\sqrt{\Delta}=\sqrt{2508}=\sqrt{4*627}=\sqrt{4}*\sqrt{627}=2\sqrt{627}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{627}}{2*1}=\frac{-50-2\sqrt{627}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{627}}{2*1}=\frac{-50+2\sqrt{627}}{2}
$