X-2/x-4=3

Solution for X-2/x-4=3 equation:

X-2/X-4=3

We move all terms to the left:

X-2/X-4-(3)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-2/X-7=0

We multiply all the terms by the denominator


X*X-7*X-2=0

We add all the numbers together, and all the variables

-7X+X*X-2=0

Wy multiply elements

X^2-7X-2=0

a = 1; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·1·(-2)
Δ = 57
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{-(-7)-\sqrt{57}}{2*1}=\frac{7-\sqrt{57}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{57}}{2*1}=\frac{7+\sqrt{57}}{2}
$