1/2x-6=2x+4

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

1/2x-6=2x+4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-2x-4-6=0

We multiply all the terms by the denominator


-2x*2x-4*2x-6*2x+1=0

Wy multiply elements

-4x^2-8x-12x+1=0

We add all the numbers together, and all the variables

-4x^2-20x+1=0

a = -4; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-4)·1
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{26}}{2*-4}=\frac{20-4\sqrt{26}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{26}}{2*-4}=\frac{20+4\sqrt{26}}{-8}
$