.03=100x-x^2

Solution for .03=100x-x^2 equation:

.03=100x-x^2

We move all terms to the left:

.03-(100x-x^2)=0

We add all the numbers together, and all the variables

-(100x-x^2)+0.03=0

We get rid of parentheses

x^2-100x+0.03=0

a = 1; b = -100; c = +0.03;
Δ = b2-4ac
Δ = -1002-4·1·0.03
Δ = 9999.88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-\sqrt{9999.88}}{2*1}=\frac{100-\sqrt{9999.88}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+\sqrt{9999.88}}{2*1}=\frac{100+\sqrt{9999.88}}{2}
$