Y=5x^2-30x+9

Solution for Y=5x^2-30x+9 equation:

=5Y^2-30Y+9

We move all terms to the left:

-(5Y^2-30Y+9)=0

We get rid of parentheses

-5Y^2+30Y-9=0

a = -5; b = 30; c = -9;
Δ = b2-4ac
Δ = 302-4·(-5)·(-9)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{5}}{2*-5}=\frac{-30-12\sqrt{5}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{5}}{2*-5}=\frac{-30+12\sqrt{5}}{-10}
$