-50+5x+10+1/6x=9

Solution for -50+5x+10+1/6x=9 equation:

-50+5x+10+1/6x=9

We move all terms to the left:

-50+5x+10+1/6x-(9)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/6x-49=0

We multiply all the terms by the denominator


5x*6x-49*6x+1=0

Wy multiply elements

30x^2-294x+1=0

a = 30; b = -294; c = +1;
Δ = b2-4ac
Δ = -2942-4·30·1
Δ = 86316
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:

$\sqrt{\Delta}=\sqrt{86316}=\sqrt{4*21579}=\sqrt{4}*\sqrt{21579}=2\sqrt{21579}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-2\sqrt{21579}}{2*30}=\frac{294-2\sqrt{21579}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+2\sqrt{21579}}{2*30}=\frac{294+2\sqrt{21579}}{60}
$