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

Solution for -5/3x+2/3-2/5x+1=0 equation:

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


(-25x)/135x^2+(-54x)/135x^2+10x/135x^2+1=0

We multiply all the terms by the denominator


(-25x)+(-54x)+10x+1*135x^2=0

We add all the numbers together, and all the variables

10x+(-25x)+(-54x)+1*135x^2=0

Wy multiply elements

135x^2+10x+(-25x)+(-54x)=0

We get rid of parentheses

135x^2+10x-25x-54x=0

We add all the numbers together, and all the variables

135x^2-69x=0

a = 135; b = -69; c = 0;
Δ = b2-4ac
Δ = -692-4·135·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-69}{2*135}=\frac{0}{270}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+69}{2*135}=\frac{138}{270}
=23/45
$