1/2x-1=12x+4

Solution for 1/2x-1=12x+4 equation:

1/2x-1=12x+4

We move all terms to the left:

1/2x-1-(12x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-12x-4-1=0

We multiply all the terms by the denominator


-12x*2x-4*2x-1*2x+1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-24x^2-10x+1=0

a = -24; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-24)·1
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*-24}=\frac{-4}{-48}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*-24}=\frac{24}{-48}
=-1/2
$