5000=x(x+100)

Solution for 5000=x(x+100) equation:

5000=x(x+100)

We move all terms to the left:

5000-(x(x+100))=0


We calculate terms in parentheses: -(x(x+100)), so:

x(x+100)

We multiply parentheses

x^2+100x

Back to the equation:

-(x^2+100x)


We get rid of parentheses

-x^2-100x+5000=0

We add all the numbers together, and all the variables

-1x^2-100x+5000=0

a = -1; b = -100; c = +5000;
Δ = b2-4ac
Δ = -1002-4·(-1)·5000
Δ = 30000
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:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100\sqrt{3}}{2*-1}=\frac{100-100\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100\sqrt{3}}{2*-1}=\frac{100+100\sqrt{3}}{-2}
$