O=-16x^2+36x+61

Solution for O=-16x^2+36x+61 equation:

=-16O^2+36O+61

We move all terms to the left:

-(-16O^2+36O+61)=0

We get rid of parentheses

16O^2-36O-61=0

a = 16; b = -36; c = -61;
Δ = b2-4ac
Δ = -362-4·16·(-61)
Δ = 5200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$O_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$O_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$O_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-20\sqrt{13}}{2*16}=\frac{36-20\sqrt{13}}{32}
$
$O_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+20\sqrt{13}}{2*16}=\frac{36+20\sqrt{13}}{32}
$