1/6x=3x-136

Solution for 1/6x=3x-136 equation:

1/6x=3x-136

We move all terms to the left:

1/6x-(3x-136)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

1/6x-3x+136=0

We multiply all the terms by the denominator


-3x*6x+136*6x+1=0

Wy multiply elements

-18x^2+816x+1=0

a = -18; b = 816; c = +1;
Δ = b2-4ac
Δ = 8162-4·(-18)·1
Δ = 665928
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:

$\sqrt{\Delta}=\sqrt{665928}=\sqrt{36*18498}=\sqrt{36}*\sqrt{18498}=6\sqrt{18498}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(816)-6\sqrt{18498}}{2*-18}=\frac{-816-6\sqrt{18498}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(816)+6\sqrt{18498}}{2*-18}=\frac{-816+6\sqrt{18498}}{-36}
$