0.6x-0.2x(x-4)=0.4(x-2)

Solution for 0.6x-0.2x(x-4)=0.4(x-2) equation:

0.6x-0.2x(x-4)=0.4(x-2)

We move all terms to the left:

0.6x-0.2x(x-4)-(0.4(x-2))=0

We multiply parentheses

-0x^2+0.6x-0x-(0.4(x-2))=0


We calculate terms in parentheses: -(0.4(x-2)), so:

0.4(x-2)

We multiply parentheses

0.4x-0.8

Back to the equation:

-(0.4x-0.8)


We add all the numbers together, and all the variables

-1x^2-0.4x-(0.4x-0.8)=0

We get rid of parentheses

-1x^2-0.4x-0.4x+0.8=0

We add all the numbers together, and all the variables

-1x^2-0.8x+0.8=0

a = -1; b = -0.8; c = +0.8;
Δ = b2-4ac
Δ = -0.82-4·(-1)·0.8
Δ = 3.84
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{-(-0.8)-\sqrt{3.84}}{2*-1}=\frac{0.8-\sqrt{3.84}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.8)+\sqrt{3.84}}{2*-1}=\frac{0.8+\sqrt{3.84}}{-2}
$