X-4/x+2=10

Solution for X-4/x+2=10 equation:

X-4/X+2=10

We move all terms to the left:

X-4/X+2-(10)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-4/X-8=0

We multiply all the terms by the denominator


X*X-8*X-4=0

We add all the numbers together, and all the variables

-8X+X*X-4=0

Wy multiply elements

X^2-8X-4=0

a = 1; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·1·(-4)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{5}}{2*1}=\frac{8-4\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{5}}{2*1}=\frac{8+4\sqrt{5}}{2}
$