Y=3x^2-60x+257

Solution for Y=3x^2-60x+257 equation:

=3Y^2-60Y+257

We move all terms to the left:

-(3Y^2-60Y+257)=0

We get rid of parentheses

-3Y^2+60Y-257=0

a = -3; b = 60; c = -257;
Δ = b2-4ac
Δ = 602-4·(-3)·(-257)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{129}}{2*-3}=\frac{-60-2\sqrt{129}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{129}}{2*-3}=\frac{-60+2\sqrt{129}}{-6}
$