X+1/2x=114

Solution for X+1/2x=114 equation:

X+1/2X=114

We move all terms to the left:

X+1/2X-(114)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-114*2X+1=0

Wy multiply elements

2X^2-228X+1=0

a = 2; b = -228; c = +1;
Δ = b2-4ac
Δ = -2282-4·2·1
Δ = 51976
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:

$\sqrt{\Delta}=\sqrt{51976}=\sqrt{4*12994}=\sqrt{4}*\sqrt{12994}=2\sqrt{12994}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-228)-2\sqrt{12994}}{2*2}=\frac{228-2\sqrt{12994}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-228)+2\sqrt{12994}}{2*2}=\frac{228+2\sqrt{12994}}{4}
$