4/2-x=9/x+12

Solution for 4/2-x=9/x+12 equation:

4/2-x=9/x+12

We move all terms to the left:

4/2-x-(9/x+12)=0


Domain of the equation: x+12)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(9/x+12)+2=0

We get rid of parentheses

-1x-9/x-12+2=0

We multiply all the terms by the denominator


-1x*x-12*x+2*x-9=0

We add all the numbers together, and all the variables

-10x-1x*x-9=0

Wy multiply elements

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

a = -1; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·(-1)·(-9)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8}{2*-1}=\frac{18}{-2}
=-9
$