5/9x+20=-1/3x+16

Solution for 5/9x+20=-1/3x+16 equation:

5/9x+20=-1/3x+16

We move all terms to the left:

5/9x+20-(-1/3x+16)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x+16)!=0

x∈R


We get rid of parentheses

5/9x+1/3x-16+20=0

We calculate fractions


15x/27x^2+9x/27x^2-16+20=0

We add all the numbers together, and all the variables

15x/27x^2+9x/27x^2+4=0

We multiply all the terms by the denominator


15x+9x+4*27x^2=0

We add all the numbers together, and all the variables

24x+4*27x^2=0

Wy multiply elements

108x^2+24x=0

a = 108; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·108·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*108}=\frac{-48}{216}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*108}=\frac{0}{216}
=0
$