7/x+3=x-3

Solution for 7/x+3=x-3 equation:

7/x+3=x-3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

7/x-x+3+3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x-x*x+7=0

Wy multiply elements

-1x^2+6x+7=0

a = -1; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-1)·7
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8}{2*-1}=\frac{2}{-2}
=-1
$