x+1/2x=105

Solution for x+1/2x=105 equation:

x+1/2x=105

We move all terms to the left:

x+1/2x-(105)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-105*2x+1=0

Wy multiply elements

2x^2-210x+1=0

a = 2; b = -210; c = +1;
Δ = b2-4ac
Δ = -2102-4·2·1
Δ = 44092
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:

$\sqrt{\Delta}=\sqrt{44092}=\sqrt{4*11023}=\sqrt{4}*\sqrt{11023}=2\sqrt{11023}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11023}}{2*2}=\frac{210-2\sqrt{11023}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11023}}{2*2}=\frac{210+2\sqrt{11023}}{4}
$