5.1=0.005x^2+0.41x-5.1

Solution for 5.1=0.005x^2+0.41x-5.1 equation:

5.1=0.005x^2+0.41x-5.1

We move all terms to the left:

5.1-(0.005x^2+0.41x-5.1)=0

We get rid of parentheses

-0.005x^2-0.41x+5.1+5.1=0

We add all the numbers together, and all the variables

-0.005x^2-0.41x+10.2=0

a = -0.005; b = -0.41; c = +10.2;
Δ = b2-4ac
Δ = -0.412-4·(-0.005)·10.2
Δ = 0.3721
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{-(-0.41)-\sqrt{0.3721}}{2*-0.005}=\frac{0.41-\sqrt{0.3721}}{-0.01}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.41)+\sqrt{0.3721}}{2*-0.005}=\frac{0.41+\sqrt{0.3721}}{-0.01}
$