2=x+10/x-7

Solution for 2=x+10/x-7 equation:

2=x+10/x-7

We move all terms to the left:

2-(x+10/x-7)=0


Domain of the equation: x-7)!=0

x∈R


We get rid of parentheses

-x-10/x+7+2=0

We multiply all the terms by the denominator


-x*x+7*x+2*x-10=0

We add all the numbers together, and all the variables

9x-x*x-10=0

Wy multiply elements

-1x^2+9x-10=0

a = -1; b = 9; c = -10;
Δ = b2-4ac
Δ = 92-4·(-1)·(-10)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{41}}{2*-1}=\frac{-9-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{41}}{2*-1}=\frac{-9+\sqrt{41}}{-2}
$