6=2x+7/3x-4

Solution for 6=2x+7/3x-4 equation:

6=2x+7/3x-4

We move all terms to the left:

6-(2x+7/3x-4)=0


Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

-2x-7/3x+4+6=0

We multiply all the terms by the denominator


-2x*3x+4*3x+6*3x-7=0

Wy multiply elements

-6x^2+12x+18x-7=0

We add all the numbers together, and all the variables

-6x^2+30x-7=0

a = -6; b = 30; c = -7;
Δ = b2-4ac
Δ = 302-4·(-6)·(-7)
Δ = 732
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:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{183}}{2*-6}=\frac{-30-2\sqrt{183}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{183}}{2*-6}=\frac{-30+2\sqrt{183}}{-12}
$