2000=(x+50)x

Solution for 2000=(x+50)x equation:

2000=(x+50)x

We move all terms to the left:

2000-((x+50)x)=0


We calculate terms in parentheses: -((x+50)x), so:

(x+50)x

We multiply parentheses

x^2+50x

Back to the equation:

-(x^2+50x)


We get rid of parentheses

-x^2-50x+2000=0

We add all the numbers together, and all the variables

-1x^2-50x+2000=0

a = -1; b = -50; c = +2000;
Δ = b2-4ac
Δ = -502-4·(-1)·2000
Δ = 10500
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:

$\sqrt{\Delta}=\sqrt{10500}=\sqrt{100*105}=\sqrt{100}*\sqrt{105}=10\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{105}}{2*-1}=\frac{50-10\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{105}}{2*-1}=\frac{50+10\sqrt{105}}{-2}
$