42/(x)-45/(x-1)+2=0

Solution for 42/(x)-45/(x-1)+2=0 equation:

42/(x)-45/(x-1)+2=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x-1)!=0

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

x!=1

x∈R


We calculate fractions


(42x-42)/(x^2-1x)+(-45x)/(x^2-1x)+2=0

We multiply all the terms by the denominator


(42x-42)+(-45x)+2*(x^2-1x)=0

We multiply parentheses

2x^2+(42x-42)+(-45x)-2x=0

We get rid of parentheses

2x^2+42x-45x-2x-42=0

We add all the numbers together, and all the variables

2x^2-5x-42=0

a = 2; b = -5; c = -42;
Δ = b2-4ac
Δ = -52-4·2·(-42)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*2}=\frac{24}{4}
=6
$