3/3x+4+5x=14x+7-6x

Solution for 3/3x+4+5x=14x+7-6x equation:

3/3x+4+5x=14x+7-6x

We move all terms to the left:

3/3x+4+5x-(14x+7-6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3/3x+5x-(8x+7)+4=0

We add all the numbers together, and all the variables

5x+3/3x-(8x+7)+4=0

We get rid of parentheses

5x+3/3x-8x-7+4=0

We multiply all the terms by the denominator


5x*3x-8x*3x-7*3x+4*3x+3=0

Wy multiply elements

15x^2-24x^2-21x+12x+3=0

We add all the numbers together, and all the variables

-9x^2-9x+3=0

a = -9; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·(-9)·3
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{21}}{2*-9}=\frac{9-3\sqrt{21}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{21}}{2*-9}=\frac{9+3\sqrt{21}}{-18}
$