Y=-16x^2+100x+86

Solution for Y=-16x^2+100x+86 equation:

=-16Y^2+100Y+86

We move all terms to the left:

-(-16Y^2+100Y+86)=0

We get rid of parentheses

16Y^2-100Y-86=0

a = 16; b = -100; c = -86;
Δ = b2-4ac
Δ = -1002-4·16·(-86)
Δ = 15504
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:

$\sqrt{\Delta}=\sqrt{15504}=\sqrt{16*969}=\sqrt{16}*\sqrt{969}=4\sqrt{969}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{969}}{2*16}=\frac{100-4\sqrt{969}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{969}}{2*16}=\frac{100+4\sqrt{969}}{32}
$