0.5(x+2)=0.1x+0.6x(X-3)

Solution for 0.5(x+2)=0.1x+0.6x(X-3) equation:

0.5(x+2)=0.1x+0.6x(x-3)

We move all terms to the left:

0.5(x+2)-(0.1x+0.6x(x-3))=0

We multiply parentheses

0.5x-(0.1x+0.6x(x-3))+1=0


We calculate terms in parentheses: -(0.1x+0.6x(x-3)), so:

0.1x+0.6x(x-3)

We multiply parentheses

0x^2+0.1x+0x

We add all the numbers together, and all the variables

x^2+1.1x

Back to the equation:

-(x^2+1.1x)


We get rid of parentheses

-x^2+0.5x-1.1x+1=0

We add all the numbers together, and all the variables

-1x^2-0.6x+1=0

a = -1; b = -0.6; c = +1;
Δ = b2-4ac
Δ = -0.62-4·(-1)·1
Δ = 4.36
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{-(-0.6)-\sqrt{4.36}}{2*-1}=\frac{0.6-\sqrt{4.36}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.6)+\sqrt{4.36}}{2*-1}=\frac{0.6+\sqrt{4.36}}{-2}
$