x+1/2x=54

Solution for x+1/2x=54 equation:

x+1/2x=54

We move all terms to the left:

x+1/2x-(54)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-54*2x+1=0

Wy multiply elements

2x^2-108x+1=0

a = 2; b = -108; c = +1;
Δ = b2-4ac
Δ = -1082-4·2·1
Δ = 11656
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:

$\sqrt{\Delta}=\sqrt{11656}=\sqrt{4*2914}=\sqrt{4}*\sqrt{2914}=2\sqrt{2914}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{2914}}{2*2}=\frac{108-2\sqrt{2914}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{2914}}{2*2}=\frac{108+2\sqrt{2914}}{4}
$