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

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

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

We move all terms to the left:

-50+5x+10+1/6x-(-6)=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-34=0

We multiply all the terms by the denominator


5x*6x-34*6x+1=0

Wy multiply elements

30x^2-204x+1=0

a = 30; b = -204; c = +1;
Δ = b2-4ac
Δ = -2042-4·30·1
Δ = 41496
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:

$\sqrt{\Delta}=\sqrt{41496}=\sqrt{4*10374}=\sqrt{4}*\sqrt{10374}=2\sqrt{10374}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-2\sqrt{10374}}{2*30}=\frac{204-2\sqrt{10374}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+2\sqrt{10374}}{2*30}=\frac{204+2\sqrt{10374}}{60}
$