85=x-1/6x

Solution for 85=x-1/6x equation:

85=x-1/6x

We move all terms to the left:

85-(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)+85=0

We get rid of parentheses

-x+1/6x+85=0

We multiply all the terms by the denominator


-x*6x+85*6x+1=0

Wy multiply elements

-6x^2+510x+1=0

a = -6; b = 510; c = +1;
Δ = b2-4ac
Δ = 5102-4·(-6)·1
Δ = 260124
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:

$\sqrt{\Delta}=\sqrt{260124}=\sqrt{4*65031}=\sqrt{4}*\sqrt{65031}=2\sqrt{65031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(510)-2\sqrt{65031}}{2*-6}=\frac{-510-2\sqrt{65031}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(510)+2\sqrt{65031}}{2*-6}=\frac{-510+2\sqrt{65031}}{-12}
$