10,000x=150x-x^2

Solution for 10,000x=150x-x^2 equation:

10.000x=150x-x^2

We move all terms to the left:

10.000x-(150x-x^2)=0

We get rid of parentheses

x^2-150x+10.000x=0

We add all the numbers together, and all the variables

x^2-140x=0

a = 1; b = -140; c = 0;
Δ = b2-4ac
Δ = -1402-4·1·0
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-140}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+140}{2*1}=\frac{280}{2}
=140
$