1/2x-12x=-3

Solution for 1/2x-12x=-3 equation:

1/2x-12x=-3

We move all terms to the left:

1/2x-12x-(-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-12x+1/2x+3=0

We multiply all the terms by the denominator


-12x*2x+3*2x+1=0

Wy multiply elements

-24x^2+6x+1=0

a = -24; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-24)·1
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*-24}=\frac{-6-2\sqrt{33}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*-24}=\frac{-6+2\sqrt{33}}{-48}
$