4x+6+3/3x=33

Solution for 4x+6+3/3x=33 equation:

4x+6+3/3x=33

We move all terms to the left:

4x+6+3/3x-(33)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x+3/3x-27=0

We multiply all the terms by the denominator


4x*3x-27*3x+3=0

Wy multiply elements

12x^2-81x+3=0

a = 12; b = -81; c = +3;
Δ = b2-4ac
Δ = -812-4·12·3
Δ = 6417
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:

$\sqrt{\Delta}=\sqrt{6417}=\sqrt{9*713}=\sqrt{9}*\sqrt{713}=3\sqrt{713}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{713}}{2*12}=\frac{81-3\sqrt{713}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{713}}{2*12}=\frac{81+3\sqrt{713}}{24}
$