-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: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-2/3X-3=0

We multiply all the terms by the denominator


X*3X-3*3X-2=0

Wy multiply elements

3X^2-9X-2=0

a = 3; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·3·(-2)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{105}}{2*3}=\frac{9-\sqrt{105}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*3}=\frac{9+\sqrt{105}}{6}
$