X+4/x-2=7

Solution for X+4/x-2=7 equation:

X+4/X-2=7

We move all terms to the left:

X+4/X-2-(7)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+4/X-9=0

We multiply all the terms by the denominator


X*X-9*X+4=0

We add all the numbers together, and all the variables

-9X+X*X+4=0

Wy multiply elements

X^2-9X+4=0

a = 1; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·1·4
Δ = 65
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{65}}{2*1}=\frac{9-\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{65}}{2*1}=\frac{9+\sqrt{65}}{2}
$