1/6x=x+5

Solution for 1/6x=x+5 equation:

1/6x=x+5

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

1/6x-x-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2-30x+1=0

a = -6; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-6)·1
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{231}}{2*-6}=\frac{30-2\sqrt{231}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{231}}{2*-6}=\frac{30+2\sqrt{231}}{-12}
$