X+1/2x=10000

Solution for X+1/2x=10000 equation:

X+1/2X=10000

We move all terms to the left:

X+1/2X-(10000)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-10000*2X+1=0

Wy multiply elements

2X^2-20000X+1=0

a = 2; b = -20000; c = +1;
Δ = b2-4ac
Δ = -200002-4·2·1
Δ = 399999992
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:

$\sqrt{\Delta}=\sqrt{399999992}=\sqrt{4*99999998}=\sqrt{4}*\sqrt{99999998}=2\sqrt{99999998}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20000)-2\sqrt{99999998}}{2*2}=\frac{20000-2\sqrt{99999998}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20000)+2\sqrt{99999998}}{2*2}=\frac{20000+2\sqrt{99999998}}{4}
$