2/33x+6=3x-4

Solution for 2/33x+6=3x-4 equation:

2/33x+6=3x-4

We move all terms to the left:

2/33x+6-(3x-4)=0


Domain of the equation: 33x!=0

x!=0/33

x!=0

x∈R


We get rid of parentheses

2/33x-3x+4+6=0

We multiply all the terms by the denominator


-3x*33x+4*33x+6*33x+2=0

Wy multiply elements

-99x^2+132x+198x+2=0

We add all the numbers together, and all the variables

-99x^2+330x+2=0

a = -99; b = 330; c = +2;
Δ = b2-4ac
Δ = 3302-4·(-99)·2
Δ = 109692
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:

$\sqrt{\Delta}=\sqrt{109692}=\sqrt{36*3047}=\sqrt{36}*\sqrt{3047}=6\sqrt{3047}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(330)-6\sqrt{3047}}{2*-99}=\frac{-330-6\sqrt{3047}}{-198}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(330)+6\sqrt{3047}}{2*-99}=\frac{-330+6\sqrt{3047}}{-198}
$