Y=-16x^2+140x+2

Solution for Y=-16x^2+140x+2 equation:

=-16Y^2+140Y+2

We move all terms to the left:

-(-16Y^2+140Y+2)=0

We get rid of parentheses

16Y^2-140Y-2=0

a = 16; b = -140; c = -2;
Δ = b2-4ac
Δ = -1402-4·16·(-2)
Δ = 19728
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:

$\sqrt{\Delta}=\sqrt{19728}=\sqrt{144*137}=\sqrt{144}*\sqrt{137}=12\sqrt{137}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-12\sqrt{137}}{2*16}=\frac{140-12\sqrt{137}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+12\sqrt{137}}{2*16}=\frac{140+12\sqrt{137}}{32}
$