Y=5x^2-60x+16

Solution for Y=5x^2-60x+16 equation:

=5Y^2-60Y+16

We move all terms to the left:

-(5Y^2-60Y+16)=0

We get rid of parentheses

-5Y^2+60Y-16=0

a = -5; b = 60; c = -16;
Δ = b2-4ac
Δ = 602-4·(-5)·(-16)
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{205}}{2*-5}=\frac{-60-4\sqrt{205}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{205}}{2*-5}=\frac{-60+4\sqrt{205}}{-10}
$