Y=-7x^2+5x+16

Solution for Y=-7x^2+5x+16 equation:

=-7Y^2+5Y+16

We move all terms to the left:

-(-7Y^2+5Y+16)=0

We get rid of parentheses

7Y^2-5Y-16=0

a = 7; b = -5; c = -16;
Δ = b2-4ac
Δ = -52-4·7·(-16)
Δ = 473
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{473}}{2*7}=\frac{5-\sqrt{473}}{14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{473}}{2*7}=\frac{5+\sqrt{473}}{14}
$