Solve the equation
$$\sqrt{25*t^2+10*t+1}-\frac{5*t+2}{\sqrt{t^2+0.4*t+0.04}}=\sum_{n=1}^{1} n$$
for $$t$$.

1. Recognize: $$\sqrt{25*t^2+10*t+1}=|5*t+1|$$ and $$\sqrt{t^2+0.4*t+0.04}=|t+0.2|$$
2. Equation becomes: $$|5*t+1|-\frac{5*t+2}{|t+0.2|}=1$$
3. Assuming positive expressions leads to: \((5*t+1)-\frac{5*t+2}{t+0.2}=1\) and simplifies to a quadratic: $$5*t^2-4*t-2=0.$$