5x+11=1/216x-20

Solution for 5x+11=1/216x-20 equation:

5x+11=1/216x-20

We move all terms to the left:

5x+11-(1/216x-20)=0


Domain of the equation: 216x-20)!=0

x∈R


We get rid of parentheses

5x-1/216x+20+11=0

We multiply all the terms by the denominator


5x*216x+20*216x+11*216x-1=0

Wy multiply elements

1080x^2+4320x+2376x-1=0

We add all the numbers together, and all the variables

1080x^2+6696x-1=0

a = 1080; b = 6696; c = -1;
Δ = b2-4ac
Δ = 66962-4·1080·(-1)
Δ = 44840736
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:

$\sqrt{\Delta}=\sqrt{44840736}=\sqrt{144*311394}=\sqrt{144}*\sqrt{311394}=12\sqrt{311394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6696)-12\sqrt{311394}}{2*1080}=\frac{-6696-12\sqrt{311394}}{2160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6696)+12\sqrt{311394}}{2*1080}=\frac{-6696+12\sqrt{311394}}{2160}
$