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+4)+20)=0

We multiply parentheses

2x^2+x-24x-(2(-2x+4)+20)=0


We calculate terms in parentheses: -(2(-2x+4)+20), so:

2(-2x+4)+20

We multiply parentheses

-4x+8+20

We add all the numbers together, and all the variables

-4x+28

Back to the equation:

-(-4x+28)


We add all the numbers together, and all the variables

2x^2-23x-(-4x+28)=0

We get rid of parentheses

2x^2-23x+4x-28=0

We add all the numbers together, and all the variables

2x^2-19x-28=0

a = 2; b = -19; c = -28;
Δ = b2-4ac
Δ = -192-4·2·(-28)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{65}}{2*2}=\frac{19-3\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{65}}{2*2}=\frac{19+3\sqrt{65}}{4}
$