1/5x+8/15=-1/3x

Solution for 1/5x+8/15=-1/3x equation:

1/5x+8/15=-1/3x

We move all terms to the left:

1/5x+8/15-(-1/3x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/5x+1/3x+8/15=0

We calculate fractions


360x^2/225x^2+45x/225x^2+75x/225x^2=0

We multiply all the terms by the denominator


360x^2+45x+75x=0

We add all the numbers together, and all the variables

360x^2+120x=0

a = 360; b = 120; c = 0;
Δ = b2-4ac
Δ = 1202-4·360·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-120}{2*360}=\frac{-240}{720}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+120}{2*360}=\frac{0}{720}
=0
$