Y=9x^2-36x^2-x+4

Solution for Y=9x^2-36x^2-x+4 equation:

=9Y^2-36Y^2-Y+4

We move all terms to the left:

-(9Y^2-36Y^2-Y+4)=0

We get rid of parentheses

-9Y^2+36Y^2+Y-4=0

We add all the numbers together, and all the variables

27Y^2+Y-4=0

a = 27; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·27·(-4)
Δ = 433
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{-(1)-\sqrt{433}}{2*27}=\frac{-1-\sqrt{433}}{54}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{433}}{2*27}=\frac{-1+\sqrt{433}}{54}
$