X+1/2x=196,5

Solution for X+1/2x=196,5 equation:

X+1/2X=196.5

We move all terms to the left:

X+1/2X-(196.5)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+1/2X-196.5=0

We multiply all the terms by the denominator


X*2X-(196.5)*2X+1=0

We multiply parentheses

X*2X-393X+1=0

Wy multiply elements

2X^2-393X+1=0

a = 2; b = -393; c = +1;
Δ = b2-4ac
Δ = -3932-4·2·1
Δ = 154441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-393)-\sqrt{154441}}{2*2}=\frac{393-\sqrt{154441}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-393)+\sqrt{154441}}{2*2}=\frac{393+\sqrt{154441}}{4}
$