6+4/x-3=3x+1/x-3

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

6+4/x-3=3x+1/x-3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/x-3x-1/x+3+3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x-3x*x+3=0

Wy multiply elements

-3x^2+6x+3=0

a = -3; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-3)·3
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{2}}{2*-3}=\frac{-6-6\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{2}}{2*-3}=\frac{-6+6\sqrt{2}}{-6}
$