x-86=24/2x

Solution for x-86=24/2x equation:

x-86=24/2x

We move all terms to the left:

x-86-(24/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+24/2x)-86=0

We get rid of parentheses

x-24/2x-86=0

We multiply all the terms by the denominator


x*2x-86*2x-24=0

Wy multiply elements

2x^2-172x-24=0

a = 2; b = -172; c = -24;
Δ = b2-4ac
Δ = -1722-4·2·(-24)
Δ = 29776
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:

$\sqrt{\Delta}=\sqrt{29776}=\sqrt{16*1861}=\sqrt{16}*\sqrt{1861}=4\sqrt{1861}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-172)-4\sqrt{1861}}{2*2}=\frac{172-4\sqrt{1861}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-172)+4\sqrt{1861}}{2*2}=\frac{172+4\sqrt{1861}}{4}
$