(12x-24)*(1.6-0.2x)=0

Solution for (12x-24)*(1.6-0.2x)=0 equation:

(12x-24)(1.6-0.2x)=0

We add all the numbers together, and all the variables

(12x-24)(-0.2x+1.6)=0

We multiply parentheses ..

(+0x^2+19.2x+0x-38.4)=0

We get rid of parentheses

0x^2+19.2x+0x-38.4=0

We add all the numbers together, and all the variables

x^2+20.2x-38.4=0

a = 1; b = 20.2; c = -38.4;
Δ = b2-4ac
Δ = 20.22-4·1·(-38.4)
Δ = 561.64
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{-(20.2)-\sqrt{561.64}}{2*1}=\frac{-20.2-\sqrt{561.64}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20.2)+\sqrt{561.64}}{2*1}=\frac{-20.2+\sqrt{561.64}}{2}
$