2(x-4)=1/4x+11-3x

Solution for 2(x-4)=1/4x+11-3x equation:

2(x-4)=1/4x+11-3x

We move all terms to the left:

2(x-4)-(1/4x+11-3x)=0


Domain of the equation: 4x+11-3x)!=0

We move all terms containing x to the left, all other terms to the right

4x-3x)!=-11

x∈R


We add all the numbers together, and all the variables

2(x-4)-(-3x+1/4x+11)=0

We multiply parentheses

2x-(-3x+1/4x+11)-8=0

We get rid of parentheses

2x+3x-1/4x-11-8=0

We multiply all the terms by the denominator


2x*4x+3x*4x-11*4x-8*4x-1=0

Wy multiply elements

8x^2+12x^2-44x-32x-1=0

We add all the numbers together, and all the variables

20x^2-76x-1=0

a = 20; b = -76; c = -1;
Δ = b2-4ac
Δ = -762-4·20·(-1)
Δ = 5856
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:

$\sqrt{\Delta}=\sqrt{5856}=\sqrt{16*366}=\sqrt{16}*\sqrt{366}=4\sqrt{366}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{366}}{2*20}=\frac{76-4\sqrt{366}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{366}}{2*20}=\frac{76+4\sqrt{366}}{40}
$