Y=36x^2+15x-6

Solution for Y=36x^2+15x-6 equation:

=36Y^2+15Y-6

We move all terms to the left:

-(36Y^2+15Y-6)=0

We get rid of parentheses

-36Y^2-15Y+6=0

a = -36; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·(-36)·6
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-33}{2*-36}=\frac{-18}{-72}
=1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+33}{2*-36}=\frac{48}{-72}
=-2/3
$