1500=x(100-x)

Solution for 1500=x(100-x) equation:

1500=x(100-x)

We move all terms to the left:

1500-(x(100-x))=0

We add all the numbers together, and all the variables

-(x(-1x+100))+1500=0


We calculate terms in parentheses: -(x(-1x+100)), so:

x(-1x+100)

We multiply parentheses

-1x^2+100x

Back to the equation:

-(-1x^2+100x)


We get rid of parentheses

1x^2-100x+1500=0

We add all the numbers together, and all the variables

x^2-100x+1500=0

a = 1; b = -100; c = +1500;
Δ = b2-4ac
Δ = -1002-4·1·1500
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{10}}{2*1}=\frac{100-20\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{10}}{2*1}=\frac{100+20\sqrt{10}}{2}
$