2/4x-4=x+1

Solution for 2/4x-4=x+1 equation:

2/4x-4=x+1

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

2/4x-x-1-4=0

We multiply all the terms by the denominator


-x*4x-1*4x-4*4x+2=0

Wy multiply elements

-4x^2-4x-16x+2=0

We add all the numbers together, and all the variables

-4x^2-20x+2=0

a = -4; b = -20; c = +2;
Δ = b2-4ac
Δ = -202-4·(-4)·2
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{3}}{2*-4}=\frac{20-12\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{3}}{2*-4}=\frac{20+12\sqrt{3}}{-8}
$