Y=-7x2+4x+9

Solution for Y=-7x2+4x+9 equation:

=-7Y^2+4Y+9

We move all terms to the left:

-(-7Y^2+4Y+9)=0

We get rid of parentheses

7Y^2-4Y-9=0

a = 7; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·7·(-9)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{67}}{2*7}=\frac{4-2\sqrt{67}}{14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{67}}{2*7}=\frac{4+2\sqrt{67}}{14}
$