6/x+4=x+3/x+7

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

6/x+4=x+3/x+7

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+7)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-3x-x*x+3=0

Wy multiply elements

-1x^2-3x+3=0

a = -1; b = -3; c = +3;
Δ = b2-4ac
Δ = -32-4·(-1)·3
Δ = 21
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{-(-3)-\sqrt{21}}{2*-1}=\frac{3-\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{21}}{2*-1}=\frac{3+\sqrt{21}}{-2}
$