2.4r(r-2)=0.4

Solution for 2.4r(r-2)=0.4 equation:

2.4r(r-2)=0.4

We move all terms to the left:

2.4r(r-2)-(0.4)=0

We add all the numbers together, and all the variables

2.4r(r-2)-0.4=0

We multiply parentheses

2r^2-4r-0.4=0

a = 2; b = -4; c = -0.4;
Δ = b2-4ac
Δ = -42-4·2·(-0.4)
Δ = 19.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-\sqrt{19.2}}{2*2}=\frac{4-\sqrt{19.2}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{19.2}}{2*2}=\frac{4+\sqrt{19.2}}{4}
$