x+1/2x-3=28

Solution for x+1/2x-3=28 equation:

x+1/2x-3=28

We move all terms to the left:

x+1/2x-3-(28)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2x-31=0

We multiply all the terms by the denominator


x*2x-31*2x+1=0

Wy multiply elements

2x^2-62x+1=0

a = 2; b = -62; c = +1;
Δ = b2-4ac
Δ = -622-4·2·1
Δ = 3836
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:

$\sqrt{\Delta}=\sqrt{3836}=\sqrt{4*959}=\sqrt{4}*\sqrt{959}=2\sqrt{959}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-2\sqrt{959}}{2*2}=\frac{62-2\sqrt{959}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+2\sqrt{959}}{2*2}=\frac{62+2\sqrt{959}}{4}
$