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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+6x*x-4=0

Wy multiply elements

6x^2+x-4=0

a = 6; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·6·(-4)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{97}}{2*6}=\frac{-1-\sqrt{97}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*6}=\frac{-1+\sqrt{97}}{12}
$