X-1/2x=12

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

X-1/2X=12

We move all terms to the left:

X-1/2X-(12)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-12*2X-1=0

Wy multiply elements

2X^2-24X-1=0

a = 2; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·2·(-1)
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{146}}{2*2}=\frac{24-2\sqrt{146}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{146}}{2*2}=\frac{24+2\sqrt{146}}{4}
$