1/(x-2)-12/x-2+35=0

Solution for 1/(x-2)-12/x-2+35=0 equation:

1/(x-2)-12/x-2+35=0


Domain of the equation: (x-2)!=0

We move all terms containing x to the left, all other terms to the right

x!=2

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/(x-2)-12/x+33=0

We calculate fractions


x/(x^2-2x)+(-12x+24)/(x^2-2x)+33=0

We multiply all the terms by the denominator


x+(-12x+24)+33*(x^2-2x)=0

We multiply parentheses

33x^2+x+(-12x+24)-66x=0

We get rid of parentheses

33x^2+x-12x-66x+24=0

We add all the numbers together, and all the variables

33x^2-77x+24=0

a = 33; b = -77; c = +24;
Δ = b2-4ac
Δ = -772-4·33·24
Δ = 2761
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{-(-77)-\sqrt{2761}}{2*33}=\frac{77-\sqrt{2761}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+\sqrt{2761}}{2*33}=\frac{77+\sqrt{2761}}{66}
$