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

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

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

We move all terms to the left:

-50+5x+1-+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-58=0

We multiply all the terms by the denominator


5x*6x-58*6x+1=0

Wy multiply elements

30x^2-348x+1=0

a = 30; b = -348; c = +1;
Δ = b2-4ac
Δ = -3482-4·30·1
Δ = 120984
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:

$\sqrt{\Delta}=\sqrt{120984}=\sqrt{20164*6}=\sqrt{20164}*\sqrt{6}=142\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-348)-142\sqrt{6}}{2*30}=\frac{348-142\sqrt{6}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-348)+142\sqrt{6}}{2*30}=\frac{348+142\sqrt{6}}{60}
$