21/2x+2=x

Solution for 21/2x+2=x equation:

21/2x+2=x

We move all terms to the left:

21/2x+2-(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+21/2x+2=0

We multiply all the terms by the denominator


-1x*2x+2*2x+21=0

Wy multiply elements

-2x^2+4x+21=0

a = -2; b = 4; c = +21;
Δ = b2-4ac
Δ = 42-4·(-2)·21
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{46}}{2*-2}=\frac{-4-2\sqrt{46}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{46}}{2*-2}=\frac{-4+2\sqrt{46}}{-4}
$