1/3x+5x=-6

Solution for 1/3x+5x=-6 equation:

1/3x+5x=-6

We move all terms to the left:

1/3x+5x-(-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/3x+6=0

We multiply all the terms by the denominator


5x*3x+6*3x+1=0

Wy multiply elements

15x^2+18x+1=0

a = 15; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·15·1
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{66}}{2*15}=\frac{-18-2\sqrt{66}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{66}}{2*15}=\frac{-18+2\sqrt{66}}{30}
$