5/2x-x=16

Solution for 5/2x-x=16 equation:

5/2x-x=16

We move all terms to the left:

5/2x-x-(16)=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+5/2x-16=0

We multiply all the terms by the denominator


-1x*2x-16*2x+5=0

Wy multiply elements

-2x^2-32x+5=0

a = -2; b = -32; c = +5;
Δ = b2-4ac
Δ = -322-4·(-2)·5
Δ = 1064
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:

$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{266}}{2*-2}=\frac{32-2\sqrt{266}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{266}}{2*-2}=\frac{32+2\sqrt{266}}{-4}
$