2x(x-0.5)-(6x+1)=(3-x)(1-x)

Solution for 2x(x-0.5)-(6x+1)=(3-x)(1-x) equation:

2x(x-0.5)-(6x+1)=(3-x)(1-x)

We move all terms to the left:

2x(x-0.5)-(6x+1)-((3-x)(1-x))=0

We add all the numbers together, and all the variables

2x(x-0.5)-(6x+1)-((-1x+3)(-1x+1))=0

We multiply parentheses

2x^2-1x-(6x+1)-((-1x+3)(-1x+1))=0

We get rid of parentheses

2x^2-1x-6x-((-1x+3)(-1x+1))-1=0

We multiply parentheses ..

2x^2-((+x^2-1x-3x+3))-1x-6x-1=0


We calculate terms in parentheses: -((+x^2-1x-3x+3)), so:

(+x^2-1x-3x+3)

We get rid of parentheses

x^2-1x-3x+3

We add all the numbers together, and all the variables

x^2-4x+3

Back to the equation:

-(x^2-4x+3)


We add all the numbers together, and all the variables

2x^2-7x-(x^2-4x+3)-1=0

We get rid of parentheses

2x^2-x^2-7x+4x-3-1=0

We add all the numbers together, and all the variables

x^2-3x-4=0

a = 1; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·1·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*1}=\frac{8}{2}
=4
$