1/2x+1+1/3x-1=20

Solution for 1/2x+1+1/3x-1=20 equation:

1/2x+1+1/3x-1=20

We move all terms to the left:

1/2x+1+1/3x-1-(20)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+1/3x-20=0

We calculate fractions


3x/6x^2+2x/6x^2-20=0

We multiply all the terms by the denominator


3x+2x-20*6x^2=0

We add all the numbers together, and all the variables

5x-20*6x^2=0

Wy multiply elements

-120x^2+5x=0

a = -120; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-120)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-120}=\frac{-10}{-240}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-120}=\frac{0}{-240}
=0
$