x+2/x-7=2

Solution for x+2/x-7=2 equation:

x+2/x-7=2

We move all terms to the left:

x+2/x-7-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+2/x-9=0

We multiply all the terms by the denominator


x*x-9*x+2=0

We add all the numbers together, and all the variables

-9x+x*x+2=0

Wy multiply elements

x^2-9x+2=0

a = 1; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·1·2
Δ = 73
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{-(-9)-\sqrt{73}}{2*1}=\frac{9-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{73}}{2*1}=\frac{9+\sqrt{73}}{2}
$