X(x+0.01)=497

Solution for X(x+0.01)=497 equation:

X(X+0.01)=497

We move all terms to the left:

X(X+0.01)-(497)=0

We multiply parentheses

X^2+0.01X-497=0

a = 1; b = 0.01; c = -497;
Δ = b2-4ac
Δ = 0.012-4·1·(-497)
Δ = 1988.0001
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{-(0.01)-\sqrt{1988.0001}}{2*1}=\frac{-0.01-\sqrt{1988.0001}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.01)+\sqrt{1988.0001}}{2*1}=\frac{-0.01+\sqrt{1988.0001}}{2}
$