1/27x-6=6x-10

Solution for 1/27x-6=6x-10 equation:

1/27x-6=6x-10

We move all terms to the left:

1/27x-6-(6x-10)=0


Domain of the equation: 27x!=0

x!=0/27

x!=0

x∈R


We get rid of parentheses

1/27x-6x+10-6=0

We multiply all the terms by the denominator


-6x*27x+10*27x-6*27x+1=0

Wy multiply elements

-162x^2+270x-162x+1=0

We add all the numbers together, and all the variables

-162x^2+108x+1=0

a = -162; b = 108; c = +1;
Δ = b2-4ac
Δ = 1082-4·(-162)·1
Δ = 12312
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:

$\sqrt{\Delta}=\sqrt{12312}=\sqrt{324*38}=\sqrt{324}*\sqrt{38}=18\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-18\sqrt{38}}{2*-162}=\frac{-108-18\sqrt{38}}{-324}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+18\sqrt{38}}{2*-162}=\frac{-108+18\sqrt{38}}{-324}
$