5x=0.1x^2

Solution for 5x=0.1x^2 equation:

5x=0.1x^2

We move all terms to the left:

5x-(0.1x^2)=0

We get rid of parentheses

-0.1x^2+5x=0

a = -0.1; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-0.1)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-0.1}=\frac{-10}{-0.2}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-0.1}=\frac{0}{-0.2}
=0
$