x+1/2(x)=27

Solution for x+1/2(x)=27 equation:

x+1/2(x)=27

We move all terms to the left:

x+1/2(x)-(27)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-27*2x+1=0

Wy multiply elements

2x^2-54x+1=0

a = 2; b = -54; c = +1;
Δ = b2-4ac
Δ = -542-4·2·1
Δ = 2908
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:

$\sqrt{\Delta}=\sqrt{2908}=\sqrt{4*727}=\sqrt{4}*\sqrt{727}=2\sqrt{727}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{727}}{2*2}=\frac{54-2\sqrt{727}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{727}}{2*2}=\frac{54+2\sqrt{727}}{4}
$