Y=3x^2+30x+15

Solution for Y=3x^2+30x+15 equation:

=3Y^2+30Y+15

We move all terms to the left:

-(3Y^2+30Y+15)=0

We get rid of parentheses

-3Y^2-30Y-15=0

a = -3; b = -30; c = -15;
Δ = b2-4ac
Δ = -302-4·(-3)·(-15)
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*-3}=\frac{30-12\sqrt{5}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+12\sqrt{5}}{2*-3}=\frac{30+12\sqrt{5}}{-6}
$