1/2x-4(2x+6)=x+1

Solution for 1/2x-4(2x+6)=x+1 equation:

1/2x-4(2x+6)=x+1

We move all terms to the left:

1/2x-4(2x+6)-(x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

1/2x-8x-(x+1)-24=0

We get rid of parentheses

1/2x-8x-x-1-24=0

We multiply all the terms by the denominator


-8x*2x-x*2x-1*2x-24*2x+1=0

Wy multiply elements

-16x^2-2x^2-2x-48x+1=0

We add all the numbers together, and all the variables

-18x^2-50x+1=0

a = -18; b = -50; c = +1;
Δ = b2-4ac
Δ = -502-4·(-18)·1
Δ = 2572
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:

$\sqrt{\Delta}=\sqrt{2572}=\sqrt{4*643}=\sqrt{4}*\sqrt{643}=2\sqrt{643}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{643}}{2*-18}=\frac{50-2\sqrt{643}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{643}}{2*-18}=\frac{50+2\sqrt{643}}{-36}
$