(2-x)*(1/2)=x-5

Solution for (2-x)*(1/2)=x-5 equation:

(2-x)(1/2)=x-5

We move all terms to the left:

(2-x)(1/2)-(x-5)=0

We add all the numbers together, and all the variables

(-1x+2)(+1/2)-(x-5)=0

We get rid of parentheses

(-1x+2)(+1/2)-x+5=0

We multiply parentheses ..

(-1x^2+2*1/2)-x+5=0

We multiply all the terms by the denominator


(-1x^2+2*1-x*2)+5*2)=0

We add all the numbers together, and all the variables

(-1x^2+2*1-x*2)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -1; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-1)·2
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*-1}=\frac{2-2\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*-1}=\frac{2+2\sqrt{3}}{-2}
$