5/6x+3=-2/3x-15

Solution for 5/6x+3=-2/3x-15 equation:

5/6x+3=-2/3x-15

We move all terms to the left:

5/6x+3-(-2/3x-15)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x-15)!=0

x∈R


We get rid of parentheses

5/6x+2/3x+15+3=0

We calculate fractions


15x/18x^2+12x/18x^2+15+3=0

We add all the numbers together, and all the variables

15x/18x^2+12x/18x^2+18=0

We multiply all the terms by the denominator


15x+12x+18*18x^2=0

We add all the numbers together, and all the variables

27x+18*18x^2=0

Wy multiply elements

324x^2+27x=0

a = 324; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·324·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*324}=\frac{-54}{648}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*324}=\frac{0}{648}
=0
$