x=-16x^2+96x+110

Solution for x=-16x^2+96x+110 equation:

x=-16x^2+96x+110

We move all terms to the left:

x-(-16x^2+96x+110)=0

We get rid of parentheses

16x^2-96x+x-110=0

We add all the numbers together, and all the variables

16x^2-95x-110=0

a = 16; b = -95; c = -110;
Δ = b2-4ac
Δ = -952-4·16·(-110)
Δ = 16065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16065}=\sqrt{9*1785}=\sqrt{9}*\sqrt{1785}=3\sqrt{1785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-3\sqrt{1785}}{2*16}=\frac{95-3\sqrt{1785}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+3\sqrt{1785}}{2*16}=\frac{95+3\sqrt{1785}}{32}
$