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+3)!=0

We move all terms containing x to the left, all other terms to the right

x!=-3

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We multiply parentheses

-x^2-3x+3x+9+7=0

We add all the numbers together, and all the variables

-1x^2+16=0

a = -1; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-1)·16
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{-(0)-8}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-1}=\frac{8}{-2}
=-4
$