x+1/2x+x-7=53

Solution for x+1/2x+x-7=53 equation:

x+1/2x+x-7=53

We move all terms to the left:

x+1/2x+x-7-(53)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x-60=0

We multiply all the terms by the denominator


2x*2x-60*2x+1=0

Wy multiply elements

4x^2-120x+1=0

a = 4; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·4·1
Δ = 14384
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:

$\sqrt{\Delta}=\sqrt{14384}=\sqrt{16*899}=\sqrt{16}*\sqrt{899}=4\sqrt{899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{899}}{2*4}=\frac{120-4\sqrt{899}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{899}}{2*4}=\frac{120+4\sqrt{899}}{8}
$