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-12=0

We multiply all the terms by the denominator


X*X-12*X+4=0

We add all the numbers together, and all the variables

-12X+X*X+4=0

Wy multiply elements

X^2-12X+4=0

a = 1; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·1·4
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{2}}{2*1}=\frac{12-8\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{2}}{2*1}=\frac{12+8\sqrt{2}}{2}
$