Y=5x^2-12x-9

Solution for Y=5x^2-12x-9 equation:

=5Y^2-12Y-9

We move all terms to the left:

-(5Y^2-12Y-9)=0

We get rid of parentheses

-5Y^2+12Y+9=0

a = -5; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-5)·9
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*-5}=\frac{-30}{-10}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*-5}=\frac{6}{-10}
=-3/5
$