Y=-3x^2+30x+7

Solution for Y=-3x^2+30x+7 equation:

=-3Y^2+30Y+7

We move all terms to the left:

-(-3Y^2+30Y+7)=0

We get rid of parentheses

3Y^2-30Y-7=0

a = 3; b = -30; c = -7;
Δ = b2-4ac
Δ = -302-4·3·(-7)
Δ = 984
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:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{246}}{2*3}=\frac{30-2\sqrt{246}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{246}}{2*3}=\frac{30+2\sqrt{246}}{6}
$