2-1/3x+2/5x-3=5

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

2-1/3x+2/5x-3=5

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1/3x+2/5x-6=0

We calculate fractions


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

We multiply all the terms by the denominator


(-5x)+6x-6*15x^2=0

We add all the numbers together, and all the variables

6x+(-5x)-6*15x^2=0

Wy multiply elements

-90x^2+6x+(-5x)=0

We get rid of parentheses

-90x^2+6x-5x=0

We add all the numbers together, and all the variables

-90x^2+x=0

a = -90; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-90)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-90}=\frac{-2}{-180}
=1/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-90}=\frac{0}{-180}
=0
$