Y=5x^2-60x+166

Solution for Y=5x^2-60x+166 equation:

=5Y^2-60Y+166

We move all terms to the left:

-(5Y^2-60Y+166)=0

We get rid of parentheses

-5Y^2+60Y-166=0

a = -5; b = 60; c = -166;
Δ = b2-4ac
Δ = 602-4·(-5)·(-166)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{70}}{2*-5}=\frac{-60-2\sqrt{70}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{70}}{2*-5}=\frac{-60+2\sqrt{70}}{-10}
$