x(x-3)=0.1

Solution for x(x-3)=0.1 equation:

x(x-3)=0.1

We move all terms to the left:

x(x-3)-(0.1)=0

We add all the numbers together, and all the variables

x(x-3)-0.1=0

We multiply parentheses

x^2-3x-0.1=0

a = 1; b = -3; c = -0.1;
Δ = b2-4ac
Δ = -32-4·1·(-0.1)
Δ = 9.4
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{-(-3)-\sqrt{9.4}}{2*1}=\frac{3-\sqrt{9.4}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{9.4}}{2*1}=\frac{3+\sqrt{9.4}}{2}
$