5/3x+19/6x=-145/18

Solution for 5/3x+19/6x=-145/18 equation:

5/3x+19/6x=-145/18

We move all terms to the left:

5/3x+19/6x-(-145/18)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

5/3x+19/6x+145/18=0

We calculate fractions


15660x^2/324x^2+540x/324x^2+1026x/324x^2=0

We multiply all the terms by the denominator


15660x^2+540x+1026x=0

We add all the numbers together, and all the variables

15660x^2+1566x=0

a = 15660; b = 1566; c = 0;
Δ = b2-4ac
Δ = 15662-4·15660·0
Δ = 2452356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2452356}=1566$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1566)-1566}{2*15660}=\frac{-3132}{31320}
=-1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1566)+1566}{2*15660}=\frac{0}{31320}
=0
$