x+2/x+14=10/x-10

Solution for x+2/x+14=10/x-10 equation:

x+2/x+14=10/x-10

We move all terms to the left:

x+2/x+14-(10/x-10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-10)!=0

x∈R


We get rid of parentheses

x+2/x-10/x+10+14=0

We multiply all the terms by the denominator


x*x+10*x+14*x+2-10=0

We add all the numbers together, and all the variables

24x+x*x-8=0

Wy multiply elements

x^2+24x-8=0

a = 1; b = 24; c = -8;
Δ = b2-4ac
Δ = 242-4·1·(-8)
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{38}}{2*1}=\frac{-24-4\sqrt{38}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{38}}{2*1}=\frac{-24+4\sqrt{38}}{2}
$