Y=3x^2-54x+13

Solution for Y=3x^2-54x+13 equation:

=3Y^2-54Y+13

We move all terms to the left:

-(3Y^2-54Y+13)=0

We get rid of parentheses

-3Y^2+54Y-13=0

a = -3; b = 54; c = -13;
Δ = b2-4ac
Δ = 542-4·(-3)·(-13)
Δ = 2760
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2760}=\sqrt{4*690}=\sqrt{4}*\sqrt{690}=2\sqrt{690}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{690}}{2*-3}=\frac{-54-2\sqrt{690}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{690}}{2*-3}=\frac{-54+2\sqrt{690}}{-6}
$