4x+1/3x=6

Solution for 4x+1/3x=6 equation:

4x+1/3x=6

We move all terms to the left:

4x+1/3x-(6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


4x*3x-6*3x+1=0

Wy multiply elements

12x^2-18x+1=0

a = 12; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·12·1
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{69}}{2*12}=\frac{18-2\sqrt{69}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{69}}{2*12}=\frac{18+2\sqrt{69}}{24}
$