0.4x^2+0.5x-0.2=24

Solution for 0.4x^2+0.5x-0.2=24 equation:

0.4x^2+0.5x-0.2=24

We move all terms to the left:

0.4x^2+0.5x-0.2-(24)=0

We add all the numbers together, and all the variables

0.4x^2+0.5x-24.2=0

a = 0.4; b = 0.5; c = -24.2;
Δ = b2-4ac
Δ = 0.52-4·0.4·(-24.2)
Δ = 38.97
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{-(0.5)-\sqrt{38.97}}{2*0.4}=\frac{-0.5-\sqrt{38.97}}{0.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{38.97}}{2*0.4}=\frac{-0.5+\sqrt{38.97}}{0.8}
$