1/3x+6x=228

Solution for 1/3x+6x=228 equation:

1/3x+6x=228

We move all terms to the left:

1/3x+6x-(228)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

6x+1/3x-228=0

We multiply all the terms by the denominator


6x*3x-228*3x+1=0

Wy multiply elements

18x^2-684x+1=0

a = 18; b = -684; c = +1;
Δ = b2-4ac
Δ = -6842-4·18·1
Δ = 467784
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:

$\sqrt{\Delta}=\sqrt{467784}=\sqrt{36*12994}=\sqrt{36}*\sqrt{12994}=6\sqrt{12994}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-684)-6\sqrt{12994}}{2*18}=\frac{684-6\sqrt{12994}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-684)+6\sqrt{12994}}{2*18}=\frac{684+6\sqrt{12994}}{36}
$