1/3x+6x=21

Solution for 1/3x+6x=21 equation:

1/3x+6x=21

We move all terms to the left:

1/3x+6x-(21)=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-21=0

We multiply all the terms by the denominator


6x*3x-21*3x+1=0

Wy multiply elements

18x^2-63x+1=0

a = 18; b = -63; c = +1;
Δ = b2-4ac
Δ = -632-4·18·1
Δ = 3897
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:

$\sqrt{\Delta}=\sqrt{3897}=\sqrt{9*433}=\sqrt{9}*\sqrt{433}=3\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{433}}{2*18}=\frac{63-3\sqrt{433}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{433}}{2*18}=\frac{63+3\sqrt{433}}{36}
$