x-1/6x=800

Solution for x-1/6x=800 equation:

x-1/6x=800

We move all terms to the left:

x-1/6x-(800)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-800*6x-1=0

Wy multiply elements

6x^2-4800x-1=0

a = 6; b = -4800; c = -1;
Δ = b2-4ac
Δ = -48002-4·6·(-1)
Δ = 23040024
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:

$\sqrt{\Delta}=\sqrt{23040024}=\sqrt{4*5760006}=\sqrt{4}*\sqrt{5760006}=2\sqrt{5760006}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4800)-2\sqrt{5760006}}{2*6}=\frac{4800-2\sqrt{5760006}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4800)+2\sqrt{5760006}}{2*6}=\frac{4800+2\sqrt{5760006}}{12}
$