1/2x=212+x

Solution for 1/2x=212+x equation:

1/2x=212+x

We move all terms to the left:

1/2x-(212+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

1/2x-(x+212)=0

We get rid of parentheses

1/2x-x-212=0

We multiply all the terms by the denominator


-x*2x-212*2x+1=0

Wy multiply elements

-2x^2-424x+1=0

a = -2; b = -424; c = +1;
Δ = b2-4ac
Δ = -4242-4·(-2)·1
Δ = 179784
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:

$\sqrt{\Delta}=\sqrt{179784}=\sqrt{36*4994}=\sqrt{36}*\sqrt{4994}=6\sqrt{4994}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-424)-6\sqrt{4994}}{2*-2}=\frac{424-6\sqrt{4994}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-424)+6\sqrt{4994}}{2*-2}=\frac{424+6\sqrt{4994}}{-4}
$