5x+11=1/216x-26

Solution for 5x+11=1/216x-26 equation:

5x+11=1/216x-26

We move all terms to the left:

5x+11-(1/216x-26)=0


Domain of the equation: 216x-26)!=0

x∈R


We get rid of parentheses

5x-1/216x+26+11=0

We multiply all the terms by the denominator


5x*216x+26*216x+11*216x-1=0

Wy multiply elements

1080x^2+5616x+2376x-1=0

We add all the numbers together, and all the variables

1080x^2+7992x-1=0

a = 1080; b = 7992; c = -1;
Δ = b2-4ac
Δ = 79922-4·1080·(-1)
Δ = 63876384
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:

$\sqrt{\Delta}=\sqrt{63876384}=\sqrt{17424*3666}=\sqrt{17424}*\sqrt{3666}=132\sqrt{3666}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7992)-132\sqrt{3666}}{2*1080}=\frac{-7992-132\sqrt{3666}}{2160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7992)+132\sqrt{3666}}{2*1080}=\frac{-7992+132\sqrt{3666}}{2160}
$