Y=-3.5x^2-0.5x+65

Solution for Y=-3.5x^2-0.5x+65 equation:

=-3.5Y^2-0.5Y+65

We move all terms to the left:

-(-3.5Y^2-0.5Y+65)=0

We get rid of parentheses

3.5Y^2+0.5Y-65=0

a = 3.5; b = 0.5; c = -65;
Δ = b2-4ac
Δ = 0.52-4·3.5·(-65)
Δ = 910.25
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{-(0.5)-\sqrt{910.25}}{2*3.5}=\frac{-0.5-\sqrt{910.25}}{7}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{910.25}}{2*3.5}=\frac{-0.5+\sqrt{910.25}}{7}
$