2/3x-8/15x=16/5

Solution for 2/3x-8/15x=16/5 equation:

2/3x-8/15x=16/5

We move all terms to the left:

2/3x-8/15x-(16/5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-8/15x-(+16/5)=0

We get rid of parentheses

2/3x-8/15x-16/5=0

We calculate fractions


(-720x^2)/1125x^2+750x/1125x^2+(-600x)/1125x^2=0

We multiply all the terms by the denominator


(-720x^2)+750x+(-600x)=0

We get rid of parentheses

-720x^2+750x-600x=0

We add all the numbers together, and all the variables

-720x^2+150x=0

a = -720; b = 150; c = 0;
Δ = b2-4ac
Δ = 1502-4·(-720)·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-150}{2*-720}=\frac{-300}{-1440}
=5/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+150}{2*-720}=\frac{0}{-1440}
=0
$