x+1/2x=159

Solution for x+1/2x=159 equation:

x+1/2x=159

We move all terms to the left:

x+1/2x-(159)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-159*2x+1=0

Wy multiply elements

2x^2-318x+1=0

a = 2; b = -318; c = +1;
Δ = b2-4ac
Δ = -3182-4·2·1
Δ = 101116
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:

$\sqrt{\Delta}=\sqrt{101116}=\sqrt{4*25279}=\sqrt{4}*\sqrt{25279}=2\sqrt{25279}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-318)-2\sqrt{25279}}{2*2}=\frac{318-2\sqrt{25279}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-318)+2\sqrt{25279}}{2*2}=\frac{318+2\sqrt{25279}}{4}
$