1/2x-x=26

Solution for 1/2x-x=26 equation:

1/2x-x=26

We move all terms to the left:

1/2x-x-(26)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/2x-26=0

We multiply all the terms by the denominator


-1x*2x-26*2x+1=0

Wy multiply elements

-2x^2-52x+1=0

a = -2; b = -52; c = +1;
Δ = b2-4ac
Δ = -522-4·(-2)·1
Δ = 2712
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:

$\sqrt{\Delta}=\sqrt{2712}=\sqrt{4*678}=\sqrt{4}*\sqrt{678}=2\sqrt{678}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-2\sqrt{678}}{2*-2}=\frac{52-2\sqrt{678}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+2\sqrt{678}}{2*-2}=\frac{52+2\sqrt{678}}{-4}
$