5x+11=1/6x+2

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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} $

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