2x+1/6x-5=0

Solution for 2x+1/6x-5=0 equation:

2x+1/6x-5=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


2x*6x-5*6x+1=0

Wy multiply elements

12x^2-30x+1=0

a = 12; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·12·1
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{213}}{2*12}=\frac{30-2\sqrt{213}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{213}}{2*12}=\frac{30+2\sqrt{213}}{24}
$