8=x+10/x-4

Solution for 8=x+10/x-4 equation:

8=x+10/x-4

We move all terms to the left:

8-(x+10/x-4)=0


Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

-x-10/x+4+8=0

We multiply all the terms by the denominator


-x*x+4*x+8*x-10=0

We add all the numbers together, and all the variables

12x-x*x-10=0

Wy multiply elements

-1x^2+12x-10=0

a = -1; b = 12; c = -10;
Δ = b2-4ac
Δ = 122-4·(-1)·(-10)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{26}}{2*-1}=\frac{-12-2\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{26}}{2*-1}=\frac{-12+2\sqrt{26}}{-2}
$