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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-8x^2+26x+1=0

a = -8; b = 26; c = +1;
Δ = b2-4ac
Δ = 262-4·(-8)·1
Δ = 708
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:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{177}}{2*-8}=\frac{-26-2\sqrt{177}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{177}}{2*-8}=\frac{-26+2\sqrt{177}}{-16}
$