(x-1/6x)=575

Solution for (x-1/6x)=575 equation:

(x-1/6x)=575

We move all terms to the left:

(x-1/6x)-(575)=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)-575=0

We get rid of parentheses

x-1/6x-575=0

We multiply all the terms by the denominator


x*6x-575*6x-1=0

Wy multiply elements

6x^2-3450x-1=0

a = 6; b = -3450; c = -1;
Δ = b2-4ac
Δ = -34502-4·6·(-1)
Δ = 11902524
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:

$\sqrt{\Delta}=\sqrt{11902524}=\sqrt{4*2975631}=\sqrt{4}*\sqrt{2975631}=2\sqrt{2975631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3450)-2\sqrt{2975631}}{2*6}=\frac{3450-2\sqrt{2975631}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3450)+2\sqrt{2975631}}{2*6}=\frac{3450+2\sqrt{2975631}}{12}
$