X-5/e+4=9

Solution for X-5/e+4=9 equation:

X-5/X+4=9

We move all terms to the left:

X-5/X+4-(9)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-5/X-5=0

We multiply all the terms by the denominator


X*X-5*X-5=0

We add all the numbers together, and all the variables

-5X+X*X-5=0

Wy multiply elements

X^2-5X-5=0

a = 1; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·1·(-5)
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{5}}{2*1}=\frac{5-3\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{5}}{2*1}=\frac{5+3\sqrt{5}}{2}
$