x+1/2x=2100

Solution for x+1/2x=2100 equation:

x+1/2x=2100

We move all terms to the left:

x+1/2x-(2100)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-2100*2x+1=0

Wy multiply elements

2x^2-4200x+1=0

a = 2; b = -4200; c = +1;
Δ = b2-4ac
Δ = -42002-4·2·1
Δ = 17639992
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:

$\sqrt{\Delta}=\sqrt{17639992}=\sqrt{4*4409998}=\sqrt{4}*\sqrt{4409998}=2\sqrt{4409998}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4200)-2\sqrt{4409998}}{2*2}=\frac{4200-2\sqrt{4409998}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4200)+2\sqrt{4409998}}{2*2}=\frac{4200+2\sqrt{4409998}}{4}
$