Y=-2x^2+35x+12

Solution for Y=-2x^2+35x+12 equation:

=-2Y^2+35Y+12

We move all terms to the left:

-(-2Y^2+35Y+12)=0

We get rid of parentheses

2Y^2-35Y-12=0

a = 2; b = -35; c = -12;
Δ = b2-4ac
Δ = -352-4·2·(-12)
Δ = 1321
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{-(-35)-\sqrt{1321}}{2*2}=\frac{35-\sqrt{1321}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1321}}{2*2}=\frac{35+\sqrt{1321}}{4}
$