5x+11=1/6x+2

Solution for 5x+11=1/6x+2 equation:

5x+11=1/6x+2

We move all terms to the left:

5x+11-(1/6x+2)=0


Domain of the equation: 6x+2)!=0

x∈R


We get rid of parentheses

5x-1/6x-2+11=0

We multiply all the terms by the denominator


5x*6x-2*6x+11*6x-1=0

Wy multiply elements

30x^2-12x+66x-1=0

We add all the numbers together, and all the variables

30x^2+54x-1=0

a = 30; b = 54; c = -1;
Δ = b2-4ac
Δ = 542-4·30·(-1)
Δ = 3036
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:

$\sqrt{\Delta}=\sqrt{3036}=\sqrt{4*759}=\sqrt{4}*\sqrt{759}=2\sqrt{759}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{759}}{2*30}=\frac{-54-2\sqrt{759}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{759}}{2*30}=\frac{-54+2\sqrt{759}}{60}
$