W(x)=-2-1/3x

Solution for W(x)=-2-1/3x equation:

(W)=-2-1/3W

We move all terms to the left:

(W)-(-2-1/3W)=0


Domain of the equation: 3W)!=0

W!=0/1

W!=0

W∈R


We add all the numbers together, and all the variables

W-(-1/3W-2)=0

We get rid of parentheses

W+1/3W+2=0

We multiply all the terms by the denominator


W*3W+2*3W+1=0

Wy multiply elements

3W^2+6W+1=0

a = 3; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·3·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{6}}{2*3}=\frac{-6-2\sqrt{6}}{6}
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{6}}{2*3}=\frac{-6+2\sqrt{6}}{6}
$