0.5x(0.8-0.2x)=0.2-0.3x

Solution for 0.5x(0.8-0.2x)=0.2-0.3x equation:

0.5x(0.8-0.2x)=0.2-0.3x

We move all terms to the left:

0.5x(0.8-0.2x)-(0.2-0.3x)=0

We add all the numbers together, and all the variables

0.5x(-0.2x+0.8)-(-0.3x+0.2)=0

We multiply parentheses

0x^2+0x-(-0.3x+0.2)=0

We get rid of parentheses

0x^2+0x+0.3x-0.2=0

We add all the numbers together, and all the variables

x^2+1.3x-0.2=0

a = 1; b = 1.3; c = -0.2;
Δ = b2-4ac
Δ = 1.32-4·1·(-0.2)
Δ = 2.49
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{-(1.3)-\sqrt{2.49}}{2*1}=\frac{-1.3-\sqrt{2.49}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.3)+\sqrt{2.49}}{2*1}=\frac{-1.3+\sqrt{2.49}}{2}
$