-4/x+17-2/3x=16

Solution for -4/x+17-2/3x=16 equation:

-4/x+17-2/3x=16

We move all terms to the left:

-4/x+17-2/3x-(16)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-4/x-2/3x+1=0

We calculate fractions


(-12x)/3x^2+(-2x)/3x^2+1=0

We multiply all the terms by the denominator


(-12x)+(-2x)+1*3x^2=0

Wy multiply elements

3x^2+(-12x)+(-2x)=0

We get rid of parentheses

3x^2-12x-2x=0

We add all the numbers together, and all the variables

3x^2-14x=0

a = 3; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·3·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*3}=\frac{28}{6}
=4+2/3
$