Y=1/3x-2x-9

Solution for Y=1/3x-2x-9 equation:

=1/3Y-2Y-9

We move all terms to the left:

-(1/3Y-2Y-9)=0


Domain of the equation: 3Y-2Y-9)!=0

Y∈R


We add all the numbers together, and all the variables

-(-2Y+1/3Y-9)=0

We get rid of parentheses

2Y-1/3Y+9=0

We multiply all the terms by the denominator


2Y*3Y+9*3Y-1=0

Wy multiply elements

6Y^2+27Y-1=0

a = 6; b = 27; c = -1;
Δ = b2-4ac
Δ = 272-4·6·(-1)
Δ = 753
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{753}}{2*6}=\frac{-27-\sqrt{753}}{12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{753}}{2*6}=\frac{-27+\sqrt{753}}{12}
$