Y=12x/9+x^2

Solution for Y=12x/9+x^2 equation:

=12Y/9+Y^2

We move all terms to the left:

-(12Y/9+Y^2)=0


Domain of the equation: 9+Y^2)!=0

We move all terms containing Y to the left, all other terms to the right

Y^2)!=-9

Y!=-9/1

Y!=-9

Y∈R


We get rid of parentheses

-Y^2-12Y/9=0

We multiply all the terms by the denominator


-Y^2*9-12Y=0

Wy multiply elements

-9Y^2-12Y=0

a = -9; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-9)·0
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{-(-12)-12}{2*-9}=\frac{0}{-18}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-9}=\frac{24}{-18}
=-1+1/3
$