Y=36x^2-196x-120

Solution for Y=36x^2-196x-120 equation:

=36Y^2-196Y-120

We move all terms to the left:

-(36Y^2-196Y-120)=0

We get rid of parentheses

-36Y^2+196Y+120=0

a = -36; b = 196; c = +120;
Δ = b2-4ac
Δ = 1962-4·(-36)·120
Δ = 55696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{55696}=236$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-236}{2*-36}=\frac{-432}{-72}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+236}{2*-36}=\frac{40}{-72}
=-5/9
$