Y=-3x^2+4x+17

Solution for Y=-3x^2+4x+17 equation:

=-3Y^2+4Y+17

We move all terms to the left:

-(-3Y^2+4Y+17)=0

We get rid of parentheses

3Y^2-4Y-17=0

a = 3; b = -4; c = -17;
Δ = b2-4ac
Δ = -42-4·3·(-17)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{55}}{2*3}=\frac{4-2\sqrt{55}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{55}}{2*3}=\frac{4+2\sqrt{55}}{6}
$