x-2x(12-1/2)=2(4-2x+20)

Solution for x-2x(12-1/2)=2(4-2x+20) equation:

x-2x(12-1/2)=2(4-2x+20)

We move all terms to the left:

x-2x(12-1/2)-(2(4-2x+20))=0

We add all the numbers together, and all the variables

x-2x(-1/2+12)-(2(-2x+24))=0

We multiply parentheses

2x^2+x-24x-(2(-2x+24))=0


We calculate terms in parentheses: -(2(-2x+24)), so:

2(-2x+24)

We multiply parentheses

-4x+48

Back to the equation:

-(-4x+48)


We add all the numbers together, and all the variables

2x^2-23x-(-4x+48)=0

We get rid of parentheses

2x^2-23x+4x-48=0

We add all the numbers together, and all the variables

2x^2-19x-48=0

a = 2; b = -19; c = -48;
Δ = b2-4ac
Δ = -192-4·2·(-48)
Δ = 745
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{-(-19)-\sqrt{745}}{2*2}=\frac{19-\sqrt{745}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{745}}{2*2}=\frac{19+\sqrt{745}}{4}
$