Y=15x^2-57x-12

Solution for Y=15x^2-57x-12 equation:

=15Y^2-57Y-12

We move all terms to the left:

-(15Y^2-57Y-12)=0

We get rid of parentheses

-15Y^2+57Y+12=0

a = -15; b = 57; c = +12;
Δ = b2-4ac
Δ = 572-4·(-15)·12
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-63}{2*-15}=\frac{-120}{-30}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+63}{2*-15}=\frac{6}{-30}
=-1/5
$