-2/5x+17=8-32/3x

Solution for -2/5x+17=8-32/3x equation:

-2/5x+17=8-32/3x

We move all terms to the left:

-2/5x+17-(8-32/3x)=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 add all the numbers together, and all the variables

-2/5x-(-32/3x+8)+17=0

We get rid of parentheses

-2/5x+32/3x-8+17=0

We calculate fractions


(-6x)/15x^2+160x/15x^2-8+17=0

We add all the numbers together, and all the variables

(-6x)/15x^2+160x/15x^2+9=0

We multiply all the terms by the denominator


(-6x)+160x+9*15x^2=0

We add all the numbers together, and all the variables

160x+(-6x)+9*15x^2=0

Wy multiply elements

135x^2+160x+(-6x)=0

We get rid of parentheses

135x^2+160x-6x=0

We add all the numbers together, and all the variables

135x^2+154x=0

a = 135; b = 154; c = 0;
Δ = b2-4ac
Δ = 1542-4·135·0
Δ = 23716
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23716}=154$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(154)-154}{2*135}=\frac{-308}{270}
=-1+19/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(154)+154}{2*135}=\frac{0}{270}
=0
$