325/100+1/2x+11/3+5/6x=511/12

Solution for 325/100+1/2x+11/3+5/6x=511/12 equation:

325/100+1/2x+11/3+5/6x=511/12

We move all terms to the left:

325/100+1/2x+11/3+5/6x-(511/12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+5/6x+325/100+11/3-(+511/12)=0

We get rid of parentheses

1/2x+5/6x+325/100+11/3-511/12=0

We calculate fractions


(-11037600x^2)/43200x^2+842400x^2/43200x^2+950400x^2/43200x^2+21600x/43200x^2+36000x/43200x^2=0

We multiply all the terms by the denominator


(-11037600x^2)+842400x^2+950400x^2+21600x+36000x=0

We add all the numbers together, and all the variables

1792800x^2+(-11037600x^2)+57600x=0

We get rid of parentheses

1792800x^2-11037600x^2+57600x=0

We add all the numbers together, and all the variables

-9244800x^2+57600x=0

a = -9244800; b = 57600; c = 0;
Δ = b2-4ac
Δ = 576002-4·(-9244800)·0
Δ = 3317760000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3317760000}=57600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57600)-57600}{2*-9244800}=\frac{-115200}{-18489600}
=2/321
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57600)+57600}{2*-9244800}=\frac{0}{-18489600}
=0
$