9/2x-65=x

Solution for 9/2x-65=x equation:

9/2x-65=x

We move all terms to the left:

9/2x-65-(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+9/2x-65=0

We multiply all the terms by the denominator


-1x*2x-65*2x+9=0

Wy multiply elements

-2x^2-130x+9=0

a = -2; b = -130; c = +9;
Δ = b2-4ac
Δ = -1302-4·(-2)·9
Δ = 16972
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:

$\sqrt{\Delta}=\sqrt{16972}=\sqrt{4*4243}=\sqrt{4}*\sqrt{4243}=2\sqrt{4243}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4243}}{2*-2}=\frac{130-2\sqrt{4243}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4243}}{2*-2}=\frac{130+2\sqrt{4243}}{-4}
$