Y=x-9/3x+2

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

=Y-9/3Y+2

We move all terms to the left:

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


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

Y∈R


We get rid of parentheses

-Y+9/3Y-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

-3Y^2-6Y+9=0

a = -3; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-3)·9
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*-3}=\frac{-6}{-6}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*-3}=\frac{18}{-6}
=-3
$