x+1/2x=850

Solution for x+1/2x=850 equation:

x+1/2x=850

We move all terms to the left:

x+1/2x-(850)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-850*2x+1=0

Wy multiply elements

2x^2-1700x+1=0

a = 2; b = -1700; c = +1;
Δ = b2-4ac
Δ = -17002-4·2·1
Δ = 2889992
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:

$\sqrt{\Delta}=\sqrt{2889992}=\sqrt{4*722498}=\sqrt{4}*\sqrt{722498}=2\sqrt{722498}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1700)-2\sqrt{722498}}{2*2}=\frac{1700-2\sqrt{722498}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1700)+2\sqrt{722498}}{2*2}=\frac{1700+2\sqrt{722498}}{4}
$