Y=5x^2-48x+27

Solution for Y=5x^2-48x+27 equation:

=5Y^2-48Y+27

We move all terms to the left:

-(5Y^2-48Y+27)=0

We get rid of parentheses

-5Y^2+48Y-27=0

a = -5; b = 48; c = -27;
Δ = b2-4ac
Δ = 482-4·(-5)·(-27)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-42}{2*-5}=\frac{-90}{-10}
=+9
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+42}{2*-5}=\frac{-6}{-10}
=3/5
$