1/2X-5=x

Solution for 1/2X-5=x equation:

1/2X-5=X

We move all terms to the left:

1/2X-5-(X)=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-5=0

We multiply all the terms by the denominator


-1X*2X-5*2X+1=0

Wy multiply elements

-2X^2-10X+1=0

a = -2; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-2)·1
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{3}}{2*-2}=\frac{10-6\sqrt{3}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{3}}{2*-2}=\frac{10+6\sqrt{3}}{-4}
$