-4+w+17-2/3w=1

Solution for -4+w+17-2/3w=1 equation:

-4+w+17-2/3w=1

We move all terms to the left:

-4+w+17-2/3w-(1)=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+12=0

We multiply all the terms by the denominator


w*3w+12*3w-2=0

Wy multiply elements

3w^2+36w-2=0

a = 3; b = 36; c = -2;
Δ = b2-4ac
Δ = 362-4·3·(-2)
Δ = 1320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{330}}{2*3}=\frac{-36-2\sqrt{330}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{330}}{2*3}=\frac{-36+2\sqrt{330}}{6}
$