27-3/2x=x

Solution for 27-3/2x=x equation:

27-3/2x=x

We move all terms to the left:

27-3/2x-(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-3/2x+27=0

We multiply all the terms by the denominator


-1x*2x+27*2x-3=0

Wy multiply elements

-2x^2+54x-3=0

a = -2; b = 54; c = -3;
Δ = b2-4ac
Δ = 542-4·(-2)·(-3)
Δ = 2892
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:

$\sqrt{\Delta}=\sqrt{2892}=\sqrt{4*723}=\sqrt{4}*\sqrt{723}=2\sqrt{723}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{723}}{2*-2}=\frac{-54-2\sqrt{723}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{723}}{2*-2}=\frac{-54+2\sqrt{723}}{-4}
$