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

Solution for 0.5x+1=(0.1x)(0.6)(x-3) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+0x)(x-3)), so:

(+0x)(x-3)

We add all the numbers together, and all the variables

(+x)(x-3)

We multiply parentheses ..

(+x^2-3x)

We get rid of parentheses

x^2-3x

Back to the equation:

-(x^2-3x)


We get rid of parentheses

-x^2+0.5x+3x+1=0

We add all the numbers together, and all the variables

-1x^2+3.5x+1=0

a = -1; b = 3.5; c = +1;
Δ = b2-4ac
Δ = 3.52-4·(-1)·1
Δ = 16.25
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{-(3.5)-\sqrt{16.25}}{2*-1}=\frac{-3.5-\sqrt{16.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.5)+\sqrt{16.25}}{2*-1}=\frac{-3.5+\sqrt{16.25}}{-2}
$