6=-0.2x^2+2.4x

Solution for 6=-0.2x^2+2.4x equation:

6=-0.2x^2+2.4x

We move all terms to the left:

6-(-0.2x^2+2.4x)=0

We get rid of parentheses

0.2x^2-2.4x+6=0

a = 0.2; b = -2.4; c = +6;
Δ = b2-4ac
Δ = -2.42-4·0.2·6
Δ = 0.96
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{-(-2.4)-\sqrt{0.96}}{2*0.2}=\frac{2.4-\sqrt{0.96}}{0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.4)+\sqrt{0.96}}{2*0.2}=\frac{2.4+\sqrt{0.96}}{0.4}
$