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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

w-2/3w+5=0

We multiply all the terms by the denominator


w*3w+5*3w-2=0

Wy multiply elements

3w^2+15w-2=0

a = 3; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·3·(-2)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{249}}{2*3}=\frac{-15-\sqrt{249}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{249}}{2*3}=\frac{-15+\sqrt{249}}{6}
$