X+1/2x=126

Solution for X+1/2x=126 equation:

X+1/2X=126

We move all terms to the left:

X+1/2X-(126)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-126*2X+1=0

Wy multiply elements

2X^2-252X+1=0

a = 2; b = -252; c = +1;
Δ = b2-4ac
Δ = -2522-4·2·1
Δ = 63496
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:

$\sqrt{\Delta}=\sqrt{63496}=\sqrt{4*15874}=\sqrt{4}*\sqrt{15874}=2\sqrt{15874}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-2\sqrt{15874}}{2*2}=\frac{252-2\sqrt{15874}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+2\sqrt{15874}}{2*2}=\frac{252+2\sqrt{15874}}{4}
$