88=x-1/6x

Solution for 88=x-1/6x equation:

88=x-1/6x

We move all terms to the left:

88-(x-1/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x-1/6x)+88=0

We get rid of parentheses

-x+1/6x+88=0

We multiply all the terms by the denominator


-x*6x+88*6x+1=0

Wy multiply elements

-6x^2+528x+1=0

a = -6; b = 528; c = +1;
Δ = b2-4ac
Δ = 5282-4·(-6)·1
Δ = 278808
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:

$\sqrt{\Delta}=\sqrt{278808}=\sqrt{4*69702}=\sqrt{4}*\sqrt{69702}=2\sqrt{69702}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(528)-2\sqrt{69702}}{2*-6}=\frac{-528-2\sqrt{69702}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(528)+2\sqrt{69702}}{2*-6}=\frac{-528+2\sqrt{69702}}{-12}
$