(1/2x)+x=500

Solution for (1/2x)+x=500 equation:

(1/2x)+x=500

We move all terms to the left:

(1/2x)+x-(500)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2x)+x-500=0

We add all the numbers together, and all the variables

x+(+1/2x)-500=0

We get rid of parentheses

x+1/2x-500=0

We multiply all the terms by the denominator


x*2x-500*2x+1=0

Wy multiply elements

2x^2-1000x+1=0

a = 2; b = -1000; c = +1;
Δ = b2-4ac
Δ = -10002-4·2·1
Δ = 999992
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:

$\sqrt{\Delta}=\sqrt{999992}=\sqrt{196*5102}=\sqrt{196}*\sqrt{5102}=14\sqrt{5102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-14\sqrt{5102}}{2*2}=\frac{1000-14\sqrt{5102}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+14\sqrt{5102}}{2*2}=\frac{1000+14\sqrt{5102}}{4}
$