4/5x+4/15+2/3x=1

Solution for 4/5x+4/15+2/3x=1 equation:

4/5x+4/15+2/3x=1

We move all terms to the left:

4/5x+4/15+2/3x-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


determiningTheFunctionDomain
4/5x+2/3x-1+4/15=0

We calculate fractions


180x^2/225x^2+180x/225x^2+150x/225x^2-1=0

We multiply all the terms by the denominator


180x^2+180x+150x-1*225x^2=0

We add all the numbers together, and all the variables

180x^2+330x-1*225x^2=0

Wy multiply elements

180x^2-225x^2+330x=0

We add all the numbers together, and all the variables

-45x^2+330x=0

a = -45; b = 330; c = 0;
Δ = b2-4ac
Δ = 3302-4·(-45)·0
Δ = 108900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{108900}=330$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(330)-330}{2*-45}=\frac{-660}{-90}
=7+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(330)+330}{2*-45}=\frac{0}{-90}
=0
$