(1/6x)+45=x

Solution for (1/6x)+45=x equation:

(1/6x)+45=x

We move all terms to the left:

(1/6x)+45-(x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/6x)-x+45=0

We add all the numbers together, and all the variables

-1x+(+1/6x)+45=0

We get rid of parentheses

-1x+1/6x+45=0

We multiply all the terms by the denominator


-1x*6x+45*6x+1=0

Wy multiply elements

-6x^2+270x+1=0

a = -6; b = 270; c = +1;
Δ = b2-4ac
Δ = 2702-4·(-6)·1
Δ = 72924
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:

$\sqrt{\Delta}=\sqrt{72924}=\sqrt{4*18231}=\sqrt{4}*\sqrt{18231}=2\sqrt{18231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-2\sqrt{18231}}{2*-6}=\frac{-270-2\sqrt{18231}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+2\sqrt{18231}}{2*-6}=\frac{-270+2\sqrt{18231}}{-12}
$