1/5x-1/2+1/3x=-17/66

Solution for 1/5x-1/2+1/3x=-17/66 equation:

1/5x-1/2+1/3x=-17/66

We move all terms to the left:

1/5x-1/2+1/3x-(-17/66)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/5x+1/3x-1/2+17/66=0

We calculate fractions


(-2970x^2)/3960x^2+1530x^2/3960x^2+792x/3960x^2+1320x/3960x^2=0

We multiply all the terms by the denominator


(-2970x^2)+1530x^2+792x+1320x=0

We add all the numbers together, and all the variables

1530x^2+(-2970x^2)+2112x=0

We get rid of parentheses

1530x^2-2970x^2+2112x=0

We add all the numbers together, and all the variables

-1440x^2+2112x=0

a = -1440; b = 2112; c = 0;
Δ = b2-4ac
Δ = 21122-4·(-1440)·0
Δ = 4460544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4460544}=2112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2112)-2112}{2*-1440}=\frac{-4224}{-2880}
=1+7/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2112)+2112}{2*-1440}=\frac{0}{-2880}
=0
$