x(x+0.01)=14

Solution for x(x+0.01)=14 equation:

x(x+0.01)=14

We move all terms to the left:

x(x+0.01)-(14)=0

We multiply parentheses

x^2+0.01x-14=0

a = 1; b = 0.01; c = -14;
Δ = b2-4ac
Δ = 0.012-4·1·(-14)
Δ = 56.0001
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{56.0001}}{2*1}=\frac{-0.01-\sqrt{56.0001}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.01)+\sqrt{56.0001}}{2*1}=\frac{-0.01+\sqrt{56.0001}}{2}
$