1/2x+33=x

Solution for 1/2x+33=x equation:

1/2x+33=x

We move all terms to the left:

1/2x+33-(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+33=0

We multiply all the terms by the denominator


-1x*2x+33*2x+1=0

Wy multiply elements

-2x^2+66x+1=0

a = -2; b = 66; c = +1;
Δ = b2-4ac
Δ = 662-4·(-2)·1
Δ = 4364
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:

$\sqrt{\Delta}=\sqrt{4364}=\sqrt{4*1091}=\sqrt{4}*\sqrt{1091}=2\sqrt{1091}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1091}}{2*-2}=\frac{-66-2\sqrt{1091}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1091}}{2*-2}=\frac{-66+2\sqrt{1091}}{-4}
$