-2/5x+17=8-11/3x

Solution for -2/5x+17=8-11/3x equation:

-2/5x+17=8-11/3x

We move all terms to the left:

-2/5x+17-(8-11/3x)=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-(-11/3x+8)+17=0

We get rid of parentheses

-2/5x+11/3x-8+17=0

We calculate fractions


(-6x)/15x^2+55x/15x^2-8+17=0

We add all the numbers together, and all the variables

(-6x)/15x^2+55x/15x^2+9=0

We multiply all the terms by the denominator


(-6x)+55x+9*15x^2=0

We add all the numbers together, and all the variables

55x+(-6x)+9*15x^2=0

Wy multiply elements

135x^2+55x+(-6x)=0

We get rid of parentheses

135x^2+55x-6x=0

We add all the numbers together, and all the variables

135x^2+49x=0

a = 135; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·135·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*135}=\frac{-98}{270}
=-49/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*135}=\frac{0}{270}
=0
$