20-x=10/X+2

Solution for 20-x=10/X+2 equation:

20-x=10/x+2

We move all terms to the left:

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


Domain of the equation: x+2)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(10/x+2)+20=0

We get rid of parentheses

-1x-10/x-2+20=0

We multiply all the terms by the denominator


-1x*x-2*x+20*x-10=0

We add all the numbers together, and all the variables

18x-1x*x-10=0

Wy multiply elements

-1x^2+18x-10=0

a = -1; b = 18; c = -10;
Δ = b2-4ac
Δ = 182-4·(-1)·(-10)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{71}}{2*-1}=\frac{-18-2\sqrt{71}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{71}}{2*-1}=\frac{-18+2\sqrt{71}}{-2}
$