1/6x-40+5x=-9

Solution for 1/6x-40+5x=-9 equation:

1/6x-40+5x=-9

We move all terms to the left:

1/6x-40+5x-(-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-31=0

We multiply all the terms by the denominator


5x*6x-31*6x+1=0

Wy multiply elements

30x^2-186x+1=0

a = 30; b = -186; c = +1;
Δ = b2-4ac
Δ = -1862-4·30·1
Δ = 34476
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:

$\sqrt{\Delta}=\sqrt{34476}=\sqrt{676*51}=\sqrt{676}*\sqrt{51}=26\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-26\sqrt{51}}{2*30}=\frac{186-26\sqrt{51}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+26\sqrt{51}}{2*30}=\frac{186+26\sqrt{51}}{60}
$