4-5x=1/6x

Solution for 4-5x=1/6x equation:

4-5x=1/6x

We move all terms to the left:

4-5x-(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

-5x-(+1/6x)+4=0

We get rid of parentheses

-5x-1/6x+4=0

We multiply all the terms by the denominator


-5x*6x+4*6x-1=0

Wy multiply elements

-30x^2+24x-1=0

a = -30; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-30)·(-1)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{114}}{2*-30}=\frac{-24-2\sqrt{114}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{114}}{2*-30}=\frac{-24+2\sqrt{114}}{-60}
$